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Talk:Elliptic curve

Issue with formulas for g2,g3 in "Elliptic curves over the complex numbers"
The formulas would be correct if the Weierstrass form y^2=4x^3 + bx + c, was unique, but it is not. For instance if we take the lattice Z[i], the lambda value is -1. The formula in the article gives values for g2,g3 which give a cubic polynomial that should cut out the correct Riemann surface. But the particular cubic is not the one coming from the differential equation satisfied by \wp, and g2,g3 should be the coefficients for that cubic. (In the Z[i] example, the g2 value appears to be transcendental, while the articles in the formula give algebraic numbers.) Perhaps someone more experienced with wiki editing could fix this?

label mistake in associativity, ellipticgroup.gif
A quick note : I find the animating demonstration of associativity to be fascinating.. but it seems to me the labels of the points are incorrect? The 'zero' is fixed (good), but then, for example 'a' + 'b' should be further from the origin than 'a' or 'b' alone? Can some kind wiki-helper get in touch with the .GIF author and double check everything is in order? — Preceding unsigned comment added by 210.55.212.205 (talk) 20:54, 16 December 2014 (UTC)

Never mind - I re-read the article, and all seems correct now! My bad :D — Preceding unsigned comment added by 210.55.212.210 (talk) 21:51, 16 December 2014 (UTC)

2003 material
I'm confused here. In the text, it states:

 * By adding a point "at infinity", we obtain the projective version of this curve; every straight line intersects this curve in three points (if the line is tangent to the curve at a point, then that point is counted twice). It is then possible to introduce a group operation on the curve with the following property: if a straight line intersects the curve at the points P, Q and R, then P + Q + R = 0 in the group.

But, for example, the x-axis intersects the curve y2 = x3 - x + 1 at only 1 point (call it P); if we consider the other two points as being infinity, this seems to require that P + inf + inf = 0. However, the x-axis is not alone in this property; several lines parallel to the x-axis also intersect at only 1 point, if we select one of these and call the point of intersection Q, then Q + inf + inf = P + inf + inf = 0 implies P = Q. Bzzzt!!!! Is the group operation restricted to those lines which actually intersect at at least two points (where tangency counts as 2 points)? Chas zzz brown 02:00 Jan 22, 2003 (UTC)

My statement above was wrong: it only that way only for algebraically closed base fields. You're right: if the fields isn't algebraically closed, we only consider lines that are tangent to the curve or intersect it in two points. AxelBoldt 17:23 Jan 22, 2003 (UTC)

I'd like to see a bit more about the group aspect of elliptic curves over finite fields (with an eye towards ECC); especially more describing an algebraic (as opposed to geometric) approach to calculating P + Q (see for a nice explanation). Should that be done at this article, at the article for elliptic curve cryptography, or at a new article? Chas zzz brown 20:04 Feb 7, 2003 (UTC)

I think it can still fit here. Can't we give the general group law formula which works for all base fields? AxelBoldt 07:37 Feb 9, 2003 (UTC)

 * Perhaps the best way to handle this would be to emphasise that the geometric picture is only valid for the real field, and then to explain that nevertheless we can make sense of things over any field by working out some algebraic formulation. The really important point here is that if two given points have rational coordinates (i.e. belong to some field), then so does the third point. This is why the group operation makes sense when defined over a given field. --Dmharvey 21:00, 28 May 2005 (UTC)

Added the restriction that K not have characteristic 3 - observe that in the diagrams in the article, there is a point P with the property P + P + P = 3P = 0 (in the y2 = x3 - x - 1 example, it's the intersection of the y-axis and the curve). Chas zzz brown 19:57 Feb 12, 2003 (UTC)

Page needs sections now. Charles Matthews 09:51, 21 Mar 2005 (UTC)

nother picture
—Sean κ. + 23:33, 27 May 2005 (UTC)

graphs of singularities
Would be nice to have graphs of singular weierstrass equations, illustrating both cusps and intersections.

On this point, it would also be nice to mention that the group law can still be defined for a singular curve, as long as we leave out the singular point (of which there can only be one -- I think). Dmharvey 17:00, 30 May 2005 (UTC)

 * Hi! There's one here:
 * http://en.wikipedia.org/wiki/Cubic_curve
 * http://en.wikipedia.org/wiki/Cubic_curve

Form of the polynomial
The article describes elliptic curves as being of the form $$y^2 = x^3 + ax + b$$. However, in Dan Bernstein's Elliptic Curve Diffie Hellman library, he uses the curve $$y^2 = x^3 + Ax^2 + x$$ where $$A = 486662$$. Is this still an elliptic curve?

 * If you think about the substitution x = x′ + c you see that there is some freedom here. That is, provided you can divide by 3 in the field, you can set c so that the Bernstein form has the coefficient of x′2 changed to 0. Charles Matthews 15:58, 26 October 2005 (UTC)

History of the term
Does anyone know why these curves are called elliptic curves? My apologies if I missed it in the article. -Monguin61 01:47, 10 December 2005 (UTC)

 * The connection is: elliptic curve => Weierstrass elliptic function (parameterises an elliptic curve) => elliptic integral => arc length of an ellipse. I tend to think of the name "elliptic curve" as a historical accident, and a poor name for the object it describes. Dmharvey 01:54, 10 December 2005 (UTC)

Rules for adding points
The article covers four cases for adding points, but it leaves out the case P+P where P is a point of inflection of the curve such that the line is horizontal or otherwise fails to intersect the curve at a third finite point. I don't want to edit the article because I'm far from an expert on this topic, but this is a fundamentally different case, is it not? --24.15.231.4 04:56, 16 December 2005 (UTC)

 * So in this case, the tangent line intersects the curve with multiplicity 3, so you get P + P + P = 0. (This includes 0 + 0 + 0 = 0.) I think you're right, the article deserves an extra diagram illustrating this, or at least some text describing it. Dmharvey 13:11, 16 December 2005 (UTC)

 * Say the tangent line is horizontal. Then P + P must be the point in infinity. Else, it must intersect the curve. I think that, given the curve
 * E: y^2 = x^3 + ax^2 + bx + c,
 * the formula of P + P is
 * ((x^4 - 2bx^2 - 8cx + b^2 - 4ac)/(4y^2), (x^6 + 2ax^5 + 5bx^4 + 20cx^3 + (-5b^2 + 20ac)x^2 + (-2ab^2 + 8a^2 c - 4bc)x + 4abc - 8 c^2 - b^3)/(8y^3)),
 * unless of course, y = 0, where 2P is the point (0,1,0) in infinity.
 * I'm not sure exactly what you are saying here, but I can give an example. Take the curve $$y^2 = x^3 - 432$$. This has a point of inflection at $$P = (12, 36)$$, which can be checked by basic calculus. The slope of the curve at P is 6, so the tangent line has equation $$y = 6x - 36$$. Solving this simultaneously with $$y^2 = x^3 - 432$$ gives the equation $$(x-12)^3 = 0$$ (as it should, because it's a point of inflection!). In other words, the tanget line intersects the curve only at P, with multiplicity 3. So in this case P + P + P = 0. In fact there should be altogether 9 points satisfying Q + Q + Q = 0; the point at infinity, P and -P, and six others with complex coordinates. Dmharvey 12:27, 25 March 2006 (UTC)
 * ((x^4 - 2bx^2 - 8cx + b^2 - 4ac)/(4y^2), (x^6 + 2ax^5 + 5bx^4 + 20cx^3 + (-5b^2 + 20ac)x^2 + (-2ab^2 + 8a^2 c - 4bc)x + 4abc - 8 c^2 - b^3)/(8y^3)),
 * unless of course, y = 0, where 2P is the point (0,1,0) in infinity.
 * I'm not sure exactly what you are saying here, but I can give an example. Take the curve $$y^2 = x^3 - 432$$. This has a point of inflection at $$P = (12, 36)$$, which can be checked by basic calculus. The slope of the curve at P is 6, so the tangent line has equation $$y = 6x - 36$$. Solving this simultaneously with $$y^2 = x^3 - 432$$ gives the equation $$(x-12)^3 = 0$$ (as it should, because it's a point of inflection!). In other words, the tanget line intersects the curve only at P, with multiplicity 3. So in this case P + P + P = 0. In fact there should be altogether 9 points satisfying Q + Q + Q = 0; the point at infinity, P and -P, and six others with complex coordinates. Dmharvey 12:27, 25 March 2006 (UTC)
 * I'm not sure exactly what you are saying here, but I can give an example. Take the curve $$y^2 = x^3 - 432$$. This has a point of inflection at $$P = (12, 36)$$, which can be checked by basic calculus. The slope of the curve at P is 6, so the tangent line has equation $$y = 6x - 36$$. Solving this simultaneously with $$y^2 = x^3 - 432$$ gives the equation $$(x-12)^3 = 0$$ (as it should, because it's a point of inflection!). In other words, the tanget line intersects the curve only at P, with multiplicity 3. So in this case P + P + P = 0. In fact there should be altogether 9 points satisfying Q + Q + Q = 0; the point at infinity, P and -P, and six others with complex coordinates. Dmharvey 12:27, 25 March 2006 (UTC)

In the article they cite 'second pane' for case 'yP = yQ' whereas in pane 2 it is obviously not the case, seems to me ?Cédric VAN ROMPAY (talk) 14:44, 12 November 2013 (UTC)

In the article: "If xP = xQ, then there are two options." But in my opinion there is also the option P=O or Q=O (O being the point at infinity). — Preceding unsigned comment added by Madyno (talk • contribs) 13:09, 29 November 2021 (UTC)

Non-singular cubic curves?
What do we call those? I've heard them being called Elliptic curves. Or non-singular curves on this form

y^2 z + axyz + byz^2 = x^3 + cx^2 z + d x z^2 + e z^3

being called elliptic curves...

Your definition appears to be different.

 * Actually, those ARE elliptic curves. But every elliptic curve on a field with Characteristic different than two or three is isomorphic (in some Morphisms that preserve the Group Structure of the curve) to a curve like the ones defined in the article. So by giving the other definition, we didn't miss any information. BrunoX 02:03, 7 December 2006 (UTC)

DAB help needed
Can someone with knowledge disambig varieties in the Isogeny section? Thanks. Simon12 02:26, 1 July 2006 (UTC)
 * I took my best guess. Change if incorrect. Simon12 03:15, 1 July 2006 (UTC)

a Mistake?
"By adding a "point at infinity", we obtain the projective version of this curve"

why one point? by Bezout theorem, this curve has exactly 3 points at infinity. 84.108.112.10 12:50, 14 April 2007 (UTC)

Doesn't this statement depend on the embadding of the elliptic curve? Liransh 19:54, 3 May 2007 (UTC)

 * Remember, in Bezout's theorem intersection points are counted with multiplicities. Homogenizing the normal form equation of the article gives $$ Y^2Z = X^3+aXZ^2+bZ^3$$. Set Y=1 and you'll find precisely one intersection of the curve and the line at infinity Z=0. And you'll easily notice that this is a triple intersection (look at the equation in the affine piece with $$Y \neq 0$$). Just to verify, if Y=0 and Z=0 you find no points. Also from the point of view of the group law this is what one should expect: the point at infinity is the neutral element of the group law, which requires it to be an inflection point for the geometric description of the group law to work.

 * And finally, yes, all this depends on the embedding. If you change that, you'll change the base point that acts as the neutral element of the group law. One way to think about the group law is that the Jacobian variety of the curve has intrinsically a group structure (not just for elliptic curves but in general). Choosing a base point on the curve gives you the corresponding Abel-Jacobi map from the curve to the Jacobian; the base point lands at the neutral element of the Jacobian. That is bijective for elliptic curves, and the group law of the curve can be defined by transporting the Jacobian's group law to the curve via this bijection. Thus changing the base point gives you a different neutral element on the curve. Stca74 14:20, 15 May 2007 (UTC)

Article rating
Stca74 12:53, 26 May 2007 (UTC)
 * Field: Clearly geometry, not algebra. Otherwise all of algebraic geometry would be under algebra, which does not make sense. And the transcendental theory of elliptic curves (over complex numbers) is even more clearly not algebra.
 * Importance: High — these objects are among the most studied in 20th and 21st century pure mathematics and have an unusually large number of links to other fields. Individual (types of) objects should not typically be of HIGH importance, but elliptic curver in my opinion deserve that.

 * Hello, as I explained on project talk page, these things tend to be both contentious and subjective. In this instance, though, I would explain why we disagree. First, elliptic curves combine not two, but THREE fields: algebraic geometry, complex analysis, number theory. Your two arguments are fine in isolation, but contradict each other: the transcendental theory of elliptic curves was finished in 19th century. Most if not all of recent research is in arithmetic, clearly not in geometry. Besides, I argued before that algebraic geometry should be a separate field, but the consensus seemed to be to leave the field alone and judge importance on the basis of categories. The reductio ad absurdum type arguments are not helpful, because clearly, we are dealing with an intentionally limited classification scheme, so contradictions are unavoidable (to me, 'Geometry'='Differential geometry', not 'Algebraic geometry'). Rather than ridiculing the classification, you can try to convince other parties why you believe it should be made more flexible. Best, Arcfrk 13:13, 26 May 2007 (UTC)
 * P.S. I agree with 'High' importance, though! It's hard to maintain stable criteria while going over dozens of articles, but thinking over it again, it's high, not mid.Arcfrk 13:35, 26 May 2007 (UTC)
 * Yes, I noticed your comment right after making the change here. And I thought about the number-theoretic importance of elliptic curves before posting my comment (that's the direction I'm coming from as well). And I think I would tend to support the separation of algebraic geometry from Geometry and Topology in the field classification. However, for as long as we do not have AG as its own field, I still think it (all of it) belongs under Geometry and Topology. The reason is that what really separates (in my mind, at least) AG from algebra is the essentially geometric viewpoint, valid also in surpisingly many arithmetic and positive-characteristic situations. And further support in my mind is provided by the essential cohomological methods which provide an extremely strong link to the topological side of Geometry and Topology. Finally, I think that from the viewpoint of a possible eventual splitting of the field, it will be easier if all of AG is for now withing one field (and again, classifying all of it with algebra would not work, as there is still a lot that is fully geometrically motivated with no arithmetic links. Cheers, Stca74 14:40, 26 May 2007 (UTC)
 * I have to admit I am somewhat perplexed by an argument that because elliptic curves are important in number theory, they should be rated within algebra. I am also puzzled why maths ratings have got anything to do with what are the topics of current research.
 * Geometry means a surprisingly large range of things, as a quick glance at Category:Geometry will soon reveal; it is certainly not equal to differential geometry for WP. Geometry guy 18:09, 30 May 2007 (UTC)

 * It only appears puzzling because it was a hypothetical discussion (if you think the transcendental theory is what is most important then you cannot claim at the same time that it's the current research that determines the importance, because the current research is in number theory). My position, hopefully, easy enough to understand, is that algebraic geometry should be a separate field. In the absence of agreement on that, elliptic curves should (in my opinion) better be filed under Algebra. However, I do not think that this in itself is of sufficient importance to spend any more time on discussion, whichever field and/or importance ratings have been assigned. Rather, we know the article is here, is fairly important, and awaits improvements. Arcfrk 05:59, 31 May 2007 (UTC)
 * "Here here" to the last sentence! Okay, you have cleared up my puzzlement, thank you for that, but not my perplexity: in the absense of field=AlgGeom, why do you prefer field=Algebra to field=Number theory? Geometry guy 18:36, 31 May 2007 (UTC)

Some comments
I am an arithmetic geometer working in the field(s?) of elliptic curves and curves of genus one. Here are my reactions to the article as currently written (it is quite good overall):

The basic definition -- "an elliptic curve is..." is close but needs even more care: first of all, if one is going to define it in earnest using the language of algebraic / arithmetic geometry (BTW, it is not clear to me that one should do this right away; more people would understand the y^2 = x^3+ax+b definition, which is not wrong, just overly concrete for some purposes), you are missing the proviso "geometrically connected." More seriously, you are missing a mention of the field of definition of the elliptic curve. As stated above, for about 100 years it has been the case that elliptic curves are interesting only over non-algebraically closed fields, so the dependence on the field should be made clear from the start. Again, a reasonable choice would be to say a bit first about elliptic curves over the rational field and then start again with a definition over an arbitrary field (with the longer Weierstrass equation).

Nitpicking point: the definition of an elliptic curve in short Weierstrass form is not insufficiently "precise"; it is simply not the definition of an elliptic curve in char. 2 or 3 that agrees with the above geometric definition (i.e., the problem is not precision; it's simply a matter of a statement which is no longer true).

The paragraph beginning "If y^2 = P(x)..." is a bit awkwardly written. In particular, somewhere in this paragraph the fact that an elliptic curve must have a rational point is forgotten. The point of the Weierstrass form is that it comes equipped with a canonical rational point (the inflection point at infinity). The other forms -- hyperelliptic quartic, plane cubic and intersection of two space quadrics -- are important alternate ways of presenting smooth curves of genus one, but in these other forms a rational point is not guaranteed (rather, a rational divisor of degree 2, 3, or 4, respectively).

Saying that the proof of FLT is by Wiles assisted by Taylor is not ideal -- the work of Taylor and Wiles was indeed spectacular, but it also built on important work of many other mathematicians: e.g. Ribet, who proved that Taniyama-Shimura implies FLT. The attribution of FLT is a complicated story which can be left to the article itself; no need to try to wing it here.

"By adding a 'point at infinity', we obtain the projective version of this curve" This could be better phrased. The projectivization of an affine curve is an easy general construction: we just homogenize the defining polynomial by inserting in each monomial term whatever power of Z brings the total degree of each term up to the maximum of the total degrees of the original terms (in this case 3, of course). Surely this is described somewhere onsite? (If not, it should be!) Then the fact that the line at infinity intersects a Weierstrass cubic in a single point can be verified. My point is that the way it is said it sounds like one knew in advance that there was one point to add. This is really not the case, since e.g. one could work with a non-Weierstrass cubic endowed with a rational point, and then the projectivization could add as many as three points.

In your definition of the group law: you never actually say what P+Q _is_, you just give defining properties. Why not say that if R is the third intersection point of P and Q with the curve, then P+Q is the third intersection point of O and R with the curve (and illustrate this with a picture)?

"One can check that this turns the curve into an abelian group, and thus into an abelian variety." Bad -- an abelian variety is a commutative group variety but not conversely (think of the additive group or the multiplicative group, e.g.). The sentence could read, "One can check that the K-rational points on E form an abelian group under +. [insert some indication that the associativity is the sticky point!]  Moreover, as a map from E x E to E, the addition law is "algebraic", i.e., given by rational functions on E, so endows E with the structure of an algebraic group (and indeed, since E is projective and geometrically connected, an abelian variety."  Or you could not say all these things -- it's not really necessary.

"The above group law can be described algebraically as well as geometrically." I object to this dichotomy here and elsewhere in the article: the above description of the group law is both algebraic _and_ geometric (and also arithmetic, since it takes fields of rationality into account). It is not necessary to perform the construction first over the real numbers and then describe it separately -- it makes sense over any field using simple, purely algebraic definitions of partial derivative, tangent line, etc. "Algebraically" and "using the following explicit equations" are not synonymous!

Elliptic curves over the complex numbers: "curious property of Weierstrass's elliptic functions..." "Curious" is unencyclopedic. Anyway, it is not explained. "Looks like" |-> "is homeomorphic to" (with a link). The reader who has made it this far will not be confused. ... "then the corresponding elliptic curves are isomorphic" And conversely!

"The isomorphism classes can be understood in a simpler way..." "Simpler" is POV.

"The complex numbers are the splitting field for polynomials" -> "the complex numbers are algebraically closed"

Drop the name "Legendre form" for the y^2 = x(x-1)(x-lambda) and give a reference (say, to Silverman) for all these formulas.

"The uniformization theorem states" |-> "The uniformization theorem implies." (It says other things as well.)

Elliptic curves over a general field: again, I wish this would be more gracefully incorporated into the above. (One way to do it is to do it over Q in a way that works over an arbitrary field, and then later to announce this.)

"One typically takes the curve to be..." This is not quite right; a curve is a curve, in the sense of arithmetic geometry. It is not simply the set of its points over the algebraic closure (although the set of points together with all morphisms from it are sufficient to recover the algebraic structure). It is better not to say anything about this subtle point than to get it a little bit wrong.

Isogeny of elliptic curve: the term "basepoint" (should be "base point") has not been used above. (Better, e.g. "the origin", or "the neutral element".) About the homomorphism property of an isogeny: moreover, the homomorphism is surjective over the algebraic closure.

"no general algorithm is known..." Elaborate on this point. There is an algorithm which we use in practice, which will work provided Shafarevich-Tate groups are finite. (The point is that having an "algorithm" that has not been proved to terminate in all cases is not the same as not having any idea at all how to start computing.)

"A formula for this rank is given by..." This is true, but the other terms in the formula are difficult both theoretically and computationally as well.

"This fact can be understood and proven with the help of some general theory..." Well, okay. I wonder whether the people who are conversant (or even potentially conversant) with etale cohomology are really looking on Wikipedia to find out how to prove Hasse's bound. Of course Hasse's proof was simpler, and there is also a relatively simple proof in Silverman's book: a reference here would be nice.

"The number of points on a specific curve..." It would be hard to compute the number of points on a nonspecific curve, wouldn't it? :)

It would be nice also to have a section on elliptic curves over local fields and reduction theory, as well as a little bit about complex multiplication.

Well, I can help out with these changes, but not tonight. 128.192.134.50 06:58, 14 August 2007 (UTC)Plclark
 * Why does an elliptic curve have to have a rational point? If it doesn't, it's not called an elliptic curve?? Tkuvho (talk) 13:30, 2 December 2010 (UTC)

Associativity
Is it obvious to everybody but me that the elliptic-curve "addition" operation is associative? How on earth did anybody ever notice, "Hey, if I define a combination operation like this, it's associative, so I can get a group!" 68.189.88.169 (talk) 22:42, 2 March 2008 (UTC)

 * It's not obvious to anyone. However, the definition of addition on elliptic curves is quite natural, if you are familiar with Bezout's theorem, and once you have a commutative binary operation with identity and inverses it's not hard to conjecture that it constitutes a group operation, and then the proof writes itself (with many computations).  The other perspective, that the points of an elliptic curve correspond to divisors of degree 0 in its Picard group, is not so obvious, but once you see it, you immediately get a group operation on the points and you start to wonder whether the other operation which you couldn't prove associative actually is, and is the same operation.  And from the definition of the Picard group it is quite easy to prove they are the same thing.

 * Neither of these qualifies as "obvious", but they are not obvious in different ways. By the way, I disclaim the usefulness of either of the links I made; the Picard group page is really utterly unhelpful.

 * Finally, you might do better by asking this question in a real mathematical forum, which this isn't. Ryan Reich (talk) 23:10, 2 March 2008 (UTC)

The article now contains a very nice animation, and purports this to provide a geometric proof of associativity. I have seen proofs of associativity with very similar diagrams (in the textbook by Niven, Zuckerman, and Montgomery, for example), but the proof includes considerably more material than currently in this wikipedia article. For example, Bezout's theorem says two cubics intersect in nine points, but one may need even more to complete the proof of associativity: such that if three cubics share eight points, then the ninth point in each of pairwise intersections is identical. Just to be clear I am only guessing that something like that would complete the proof. (By the way, in the diagram the three cubics are (1) the curve, and (2) the three nearly vertical lines and (3) the three nearly horizontal lines. The ninth point in question is the central point.)  In other words, the article is now wrong: a geometric proof is not supplied. I will try to remove this claim, without hindering the importance and intuition of the animation. I hope that somebody else can supply the missing parts of the proof. DRLB (talk) 15:50, 13 May 2013 (UTC)

Sorry to bother you, but it is written "The article now contains a very nice animation" at 15:50, 13 May 2013 (UTC), but I can't find the "animation", or perhaps it stopped being animated and is just a simple picture. Please fix or explain ... (Peter10003 (talk) 16:49, 28 July 2017 (UTC))

 * I have restored the (admittedly a bit crude) animation at Elliptic curve. It had been removed a few days ago without explanation. I have changed the layout a bit to keep the animation from flowing into the following section. Please check. Tea2min (talk) 07:29, 30 July 2017 (UTC)

I really like the animation, and I think it nicely illustrates the Cayley-Bacharach theorem (though not its proof). However, for the elliptic curve group law, it seems a little off, because O is not an inflection point. (True, any point can serve as O, but if O is a non-inflection points, the chord-and-tangent law does not define addition, if I recall correctly.) In the animation, O does not look like an inflection point. Not sure who knows how to modify the animation. DRLB (talk) 00:58, 31 July 2017 (UTC)

 * Thank you for your comment. I see now that that was the reason the animation had been removed, see 's comment in the section below. As of now, I think it would be best to remove the section Elliptic curve completely until the animation gets fixed as the section doesn't make much sense without the animation, IMO. Tea2min (talk) 07:01, 2 August 2017 (UTC)

First sentence
Did we lose something along the way? The O in the first sentence doesn't seem to help with the definition. Perhaps there was some characteristic of O that is missing? (John User:Jwy talk) 23:00, 19 October 2008 (UTC)

The requirement for a point O forces the curve to have a rational projective point. Curves without any rational projective points are not elliptic curves. In practice, most of the time, the curve is chosen to have a single point at infinity which is taken for O, but this is not a requirement. 83.159.7.181 (talk) 10:13, 17 July 2012 (UTC)

A typo?
I'm not an algebraic geometer/number theorist, but this looks wrong: "For prime numbers ℓ not dividing N, the coefficient \scriptstyle a(\ell) of the form equals ℓ – the number of solutions of the minimal equation of the curve modulo ℓ." Shouldn't it be "...equals aℓ – the number of solutions..."? If so, probably needs a reference — Preceding unsigned comment added by 203.24.207.178 (talk) 06:10, 31 July 2012 (UTC)

Hey, Deltahedron...
why didn't you like my edit?

The link to Tunnell, as it stands, isn't useful. The referenced Tunnell isn't even one of those mentioned in the disambiguation page, whereas I proposed an useful link.

At least an explanation is in order instead of just bluntly undoing. — Preceding unsigned comment added by 89.247.124.39 (talk) 13:21, 24 December 2012 (UTC)

 * I don't understand this.  made this change to link to Tunnell's theorem and that link is still there.  I assume that  is the same person?  My subsequent change was quite unrelated.  It would help if the anonymous editor(s) would (1) explain exactly what it is they are objecting to here, (2) address personal messages to other editors on User talk pages not article talk pages, and (3) consider acquiring their own editor name to facilitate communication with other users.  Deltahedron (talk) 14:00, 24 December 2012 (UTC)

Original anonymous here: Oops -- I stand corrected. I can't reproduce the problem now: the new link is there. Let's assume it was my browser playing nasty caching tricks on me.

Please accept my apologies — Preceding unsigned comment added by 89.247.13.63 (talk) 10:20, 26 December 2012 (UTC)

 * Not a problem. But please do consider Why create an account?.  Deltahedron (talk) 17:28, 26 December 2012 (UTC)

What's E(Q)?
I came here looking to remind myself how the rational points of an elliptic curve were defined, and was annoyed that halfway through the article the symbols E(Q) is introduced without explanation. For lots of people this would mean nothing. I'm enough of a mathematician that I know it means the rational points of the elliptic curve... however, the article should explain this and say exactly what the rational points are. (For example, presumably the point at infinity is a rational point.) — Preceding unsigned comment added by John Baez (talk • contribs)

Mistakes
Section 3 seems to contain some fundamental mistakes. The formulas linking $g_2$, $g_3$ and $\Delta$ to $\lambda$ are clearly wrong, since the former are modular forms (transforming with a non-trivial weight) and the latter a modular function (transforming without a weight). I am not sure how to fix this.129.16.128.185 (talk) 14:07, 9 June 2016 (UTC)

Statement needs elaboration (or deletion)
Under the section Elliptic curves over the complex numbers, this passage appears:

"the Weierstrass functions are naturally defined on a torus T = C/Λ. This torus may be embedded in the complex projective plane by means of the map

 * $$z \mapsto [1 :\wp(z) : \wp'(z)]$$

This map is a group isomorphism, carrying the natural group structure of the torus into the projective plane."

But it is not clear what it means to say that the map $$z \mapsto [1 :\wp(z) : \wp'(z)]$$ is a group isomorphism.

The projective plane does not carry a group structure of its own. So in what sense does the image of this map $$z \mapsto [1 :\wp(z) : \wp'(z)]$$ even have a group structure?

Of course, any bijection from a group to a set can be used to transfer the group structure of the group to one on its image. But in this case it is confusing to call that an isomorphism (even though it is one): It is just a map used to copy a group from one set onto another set.

I hope someone more knowledgeable than I will improve the exposition here.Daqu (talk) 19:07, 5 September 2016 (UTC)

 * These sentences are talking about the relation between the torus C / Λ and the cubic curve $$y^2 = 4x^3 - g_2x - g_3$$. I edited the article; hopefully it is clearer.  Ozob (talk) 02:53, 6 September 2016 (UTC)

 * Thank you, Ozob! It looks much clearer now.Daqu (talk) 07:41, 6 September 2016 (UTC)

External links modified
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On the "minus points" in the gif
There is the following mistake in the gif:

The "minus points", e.g. -(a+b), are incorrect. The labeling is based on the misconception that "three points on a line add up to 0". This is however only true if 0 is itself an inflection point.

That it is not true otherwise can easily be seen by considering the tangent at 0 itself.

The fix is that first the "minus labels" should be deleted and then also a line from 0 trough the middle point (currently labeled -(a+b+c)) should be drawn. The third intersection is then a+b+c. — Preceding unsigned comment added by Claus from Leipzig (talk • contribs) 20:22, 21 June 2017 (UTC)

I have now deleted the incorrect gif. It would of course nice to have a correct one.Claus from Leipzig (talk) 08:11, 21 July 2017 (UTC)

 * I had missed your comment when I restored the animation a few days ago, sorry. I think it would be best to remove the section Elliptic curve completely until the animation gets fixed as it really doesn't make much sense without the animation. See section above, too. Tea2min (talk) 07:05, 2 August 2017 (UTC)

I just deleted this section.Claus from Leipzig (talk) 20:13, 8 August 2017 (UTC)

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Elliptic curves over complex numbers
Surely the formulas for g_2 and g_3 here need to be multiplied by something. The modular lambda function :H -> C is invariant under all of \Gamma(2) but g_2 and g_3 are not, so they cannot be polynomials in \lambda.

I think for instance the formula for g_3 needs to be multipled by the modular form -4 \pi^6 \theta_3(0,1+\tau)^{12} (after replacing \lambda by 1-\lambda).

It's nicely written and I don't advocate increasing the complexity, but surely simplifying things to the point of incorrectness can't have been the best choice. Createangelos (talk) 09:56, 11 February 2019 (UTC)

Question about elliptic curve over field of characteristic 3
Why is the coefficient of the x3 term shown as 4? Doesn't 4=1 in a field of characteristic 3? MeanStandev (talk) 18:07, 27 June 2020 (UTC)

How is a rank determined to be exact?
In Elliptic curves over the rational numbers:The structure of rational points the largest known rank is ">=28". There is no mention of how it is then determined how this might become "=28". Is this worth mentioning?

Darcourse (talk) 04:50, 26 April 2022 (UTC)

Wrong John Cremona in references
The reference for the book "Algorithms for Modular Elliptic Curves" links the author to the article on the Maltese politician John Joseph Cremona (https://en.wikipedia.org/wiki/John_Cremona). The author is in fact John E. Cremona, emeritus professor at the University of Warwick (https://warwick.ac.uk/fac/sci/maths/people/staff/john_cremona/, https://johncremona.github.io/). — Preceding unsigned comment added by Autoplunger (talk • contribs) 03:59, 13 May 2022 (UTC)

 * Thanks, I fixed it. Prame tan (talk) 07:48, 3 April 2023 (UTC)

The structure of rational points: Move proof of Mordell–Weil theorem
This looks nice, but detailed discussion of the proof and its implications seems like it should belong on the Mordell–Weil theorem page rather than in a subsection here. To be specific, I think the part from "The proof of the theorem involves two parts." to "The theorem however doesn't provide a method to determine any representatives of E(Q)/mE(Q)." can be moved. Kclisp (talk) 17:12, 26 March 2023 (UTC)

This means what???
The introductory section contains this passage:

"The curve is required to be non-singular, which means that the curve has no cusps or self-intersections. (This is equivalent to the condition $4a^{3} + 27b^{2} ≠ 0$, that is, being square-free in $x$.)"

1. What is it that is supposedly "square-free in x" ???

2. What does "square-free in x" mean here?

I hope that someone familiar with the subject and also familiar with writing clearly in English can fix this.

title: Talk:Elliptic curve


text:
Glottal stop

The glottal stop or glottal plosive is a type of consonantal sound used in many spoken languages, produced by obstructing airflow in the vocal tract or, more precisely, the glottis. The symbol in the International Phonetic Alphabet that represents this sound is ⟨ʔ⟩.

As a result of the obstruction of the airflow in the glottis, the glottal vibration either stops or becomes irregular with a low rate and sudden drop in intensity.

Features
Features of the glottal stop:

 * It has no phonation at all, as there is no airflow through the glottis. It is voiceless, however, in the sense that it is produced without vibrations of the vocal cords.

Writing

In the traditional romanization of many languages, such as Arabic, the glottal stop is transcribed with the apostrophe ʼ|$\langleʼ\rangle$ or the symbol ʾ|$⟨ʾ⟩$, which is the source of the IPA character ⟨ʔ⟩. In many Polynesian languages that use the Latin alphabet, however, the glottal stop is written with a rotated apostrophe, $⟨⟩$ (called ʻokina in Hawaiian and Samoan), which is commonly used to transcribe the Arabic ayin as well (also $⟨⟩$) and is the source of the IPA character for the voiced pharyngeal fricative ⟨ʕ⟩. In Malay the glottal stop is represented by the letter $⟨k⟩$ (at the end of words), in Võro and Maltese by $⟨q⟩$. Another way of writing the glottal stop is the saltillo $⟨Ꞌ ꞌ⟩$, used in languages such as Tlapanec and Rapa Nui.

Other scripts also have letters used for representing the glottal stop, such as the Hebrew letter aleph $⟨⟩$ and the Cyrillic letter palochka $⟨Ӏ⟩$, used in several Caucasian languages. The Arabic script uses hamza $⟨ء⟩$, which can appear both as a diacritic and as an independent letter (though not part of the alphabet). In Tundra Nenets, it is represented by the letters apostrophe $⟨ʼ⟩$ and double apostrophe $⟨ˮ⟩$. In Japanese, glottal stops occur at the end of interjections of surprise or anger and are represented by the character $⟨っ⟩$.

In the graphic representation of most Philippine languages, the glottal stop has no consistent symbolization. In most cases, however, a word that begins with a vowel-letter (e.g. Tagalog aso, "dog") is always pronounced with an unrepresented glottal stop before that vowel (as in Modern German and Hausa). Some orthographies use a hyphen instead of the reverse apostrophe if the glottal stop occurs in the middle of the word (e.g. Tagalog pag-ibig, "love"; or Visayan gabi-i, "night"). If it occurs in the end of a word, the last vowel can be written with a circumflex accent (known as the pakupyâ) if both a stress and a glottal stop occur in the final vowel (e.g. basâ, "wet") or a grave accent (known as the paiwà) if the glottal stop occurs at the final vowel, but the stress occurs at the penultimate syllable (e.g. batà, "child").

Some Canadian indigenous languages, especially some of the Salishan languages, have adopted the IPA letter $⟨ʔ⟩$ into their orthographies. In some of them, it occurs as a casing pair, $⟨Ɂ⟩$ and $⟨ɂ⟩$. The digit $⟨7⟩$ or a question mark is sometimes substituted for $⟨ʔ⟩$, and is preferred in languages such as Squamish. SENĆOŦEN – whose alphabet is mostly unique from other Salish languages – contrastly uses the comma $\langle,\rangle$ to represent the glottal stop, though it is optional.

In 2015, two women in the Northwest Territories challenged the territorial government over its refusal to permit them to use the letter $⟨ʔ⟩$ in their daughters' names: Sahaiʔa, a Chipewyan name, and Sakaeʔah, a Slavey name (the two names are actually cognates). The territory argued that territorial and federal identity documents were unable to accommodate the character. The women registered the names with hyphens instead of the $⟨ʔ⟩$, while continuing to challenge the policy.

In the Crow language, the glottal stop is written as a question mark $⟨?⟩$. The only instance of the glottal stop in Crow is as a question marker morpheme at the end of a sentence.

Use of the glottal stop is a distinct characteristic of the Southern Mainland Argyll dialects of Scottish Gaelic. In such a dialect, the standard Gaelic phrase Tha Gàidhlig agam ("I speak Gaelic"), would be rendered Tha Gàidhlig a'am.

Replacement of /t/
In English, the glottal stop occurs as an open juncture (for example, between the vowel sounds in uh-oh!, ) and allophonically in t-glottalization. In British English, the glottal stop is most familiar in the Cockney pronunciation of "butter" as "bu'er". Geordie English often uses glottal stops for t, k, and p, and has a unique form of glottalization. Additionally, there is the glottal stop as a null onset for English; in other words, it is the non-phonemic glottal stop occurring before isolated or initial vowels.

Often a glottal stop happens at the beginning of vowel phonation after a silence.

Although this segment is not a phoneme in English, it occurs phonetically in nearly all dialects of English, as an allophone of in the syllable coda. Speakers of Cockney, Scottish English and several other British dialects also pronounce an intervocalic between vowels as in city. In Received Pronunciation, a glottal stop is inserted before a tautosyllabic voiceless stop: stop, that, knock, watch, also leap, soak, help, pinch.

In American English, a "t" is usually not aspirated in syllables ending either in a vowel + "t", such as "cat" or "outside"; or in a "t" + unstressed vowel + "n", such as "mountain" or "Manhattan". This is referred to as a "held t" as the airflow is stopped by tongue at the ridge behind the teeth. However, there is a trend of younger speakers in the Mid-Atlantic states to replace the "held t" with a glottal stop, so that "Manhattan" sounds like "Man-haʔ-in" or "Clinton" like "Cli(n)ʔ-in", where "ʔ" is the glottal stop. This may have crossed over from African American Vernacular English, particularly that of New York City.

Before initial vowels
Most English speakers today often use a glottal stop before the initial vowel of words beginning with a vowel, particularly at the beginning of sentences or phrases or when a word is emphasized. This is also known as "hard attack". Traditionally in Received Pronunciation, "hard attack" was seen as a way to emphasize a word. Today, in British, American and other varieties of English, it is increasingly used not only to emphasize but also simply to separate two words, especially when the first word ends in a glottal stop.

Occurrence in other languages
In many languages that do not allow a sequence of vowels, such as Persian, the glottal stop may be used epenthetically to prevent such a hiatus. There are intricate interactions between falling tone and the glottal stop in the histories of such languages as Danish (see stød), Cantonese and Thai.

In many languages, the unstressed intervocalic allophone of the glottal stop is a creaky-voiced glottal approximant. It is known to be contrastive in only one language, Gimi, in which it is the voiced equivalent of the stop.

The table below demonstrates how widely the sound of glottal stop is found among the world's spoken languages:

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Glottal stop


text:
1934 in film

The following is an overview of 1934 in film, including significant events, a list of films released and notable births and deaths.

Top-grossing films (U.S.)
The top ten 1934 released films by box office gross in North America are as follows:

Events

 * January 26 – Samuel Goldwyn (formerly of Metro-Goldwyn-Mayer) purchases the film rights to The Wonderful Wizard of Oz from the L. Frank Baum estate for $40,000.
 * February 19 – Bob Hope marries Dolores Reade.
 * April 19 – Fox Studios releases Stand Up and Cheer!, with five-year-old Shirley Temple in a relatively minor role. Shirley steals the film and Fox, which had been near bankruptcy, finds itself owning a goldmine.
 * May 18 – Paramount releases Little Miss Marker, with Shirley Temple, on loan from Fox, in the title role.
 * June 13 – An amendment to the Production Code establishes the Production Code Administration, and requires all films to obtain a certificate of approval before being released.
 * July 28 – Canadian-born actress Marie Dressler, best known for starring in films such as Min and Bill and Emma, dies from cancer in Santa Barbara, California at the age of 65. For her performance in Min and Bill, Dressler received the Academy Award for Best Actress.
 * October 19 – Fred Astaire and Ginger Rogers wham audiences again with their first joint starring roles in The Gay Divorcee, grossing $1.8 million to add to the $1.5 million earned by Flying Down to Rio released at the end of 1933.
 * November 12 – The musical Babes in Toyland debuts, starring Stan Laurel and Oliver Hardy as comic relief.
 * December 11 – Fox releases the Sol M. Wurtzel production of Bright Eyes, starring their hot new property, Shirley Temple. Shirley sings "On the Good Ship Lollipop", and wins the first Academy Award ever given to a child, for her endearing portrayal of Shirley Blake.

Academy Awards
The 7th Academy Awards was held on February 27, 1935, at the Biltmore Hotel in Los Angeles. They were hosted by Irvin S. Cobb. For the first time, the Academy standardized the practice – still in effect, notwithstanding changes to the 93rd and 94th Academy Awards as a result of the COVID-19 pandemic – that the award eligibility period for a film would be the preceding calendar year.

Most nominations: One Night of Love (Columbia Pictures) – 6

Major Awards
 * Best Picture: It Happened One Night – Columbia Pictures
 * Best Director: Frank Capra – It Happened One Night
 * Best Actor: Clark Gable – It Happened One Night
 * Best Actress: Claudette Colbert – It Happened One Night

Most Awards: It Happened One Night – 5

It Happened One Night became the first film to perform a "clean sweep" of the top five award categories: Best Picture, Best Director, Best Actor, Best Actress, and Best Screenplay. This feat would later be duplicated by One Flew Over the Cuckoo's Nest in 1976 and The Silence of the Lambs in 1992. It also was the first romantic comedy to be named Best Picture.

1934 film releases
United States unless stated

January–March

 * January 1934
 * 6 January
 * The Big Shakedown
 * 19 January
 * Frontier Marshal
 * 22 January
 * The Lucky Texan
 * 26 January
 * Four Frightened People
 * You Can't Buy Everything
 * Unknown
 * Colonel Blood
 * February 1934
 * 1 February
 * All of Me
 * 2 February
 * Carolina
 * 3 February
 * Dark Hazard
 * I've Got Your Number
 * 9 February
 * Les Misérables (France)
 * The Rise of Catherine the Great (GB)
 * Six of a Kind
 * The Tars (Netherlands)
 * 10 February
 * Mandalay
 * 14 February
 * Fashions of 1934
 * 16 February
 * The Cat and the Fiddle
 * The Lost Patrol
 * 22 February
 * It Happened One Night
 * 23 February
 * Bolero
 * Death Takes a Holiday
 * 25 February
 * Managed Money
 * March 1934
 * 3 March
 * David Harum
 * 17 March
 * Jimmy the Gent
 * 30 March
 * Riptide
 * Spitfire
 * 31 March
 * Gambling Lady
 * Wonder Bar

April–June

 * April 1934
 * 5 April
 * You're Telling Me!
 * 7 April
 * The House of Rothschild
 * 9 April
 * Glamour
 * 10 April
 * Viva Villa!
 * Whirlpool
 * 15 April
 * City Limits
 * 16 April
 * Tarzan and His Mate
 * 26 April
 * We're Not Dressing
 * 27 April
 * Liliom
 * May 1934
 * 1 May
 * The Last Round-Up
 * Little Man, What Now?
 * 2 May
 * Le Grand Jeu
 * 3 May
 * Twentieth Century
 * 4 May
 * Manhattan Melodrama
 * Stand Up and Cheer!
 * 9 May
 * Sadie McKee
 * 15 May
 * The Man from Utah
 * 18 May
 * The Black Cat
 * Born to Be Bad
 * Thirty-Day Princess
 * 25 May
 * The Thin Man
 * 26 May
 * Twenty Million Sweethearts
 * 31 May
 * The Key
 * June 1934
 * 1 June
 * Little Miss Marker
 * 2 June
 * Fog Over Frisco
 * Operator 13
 * 4 June
 * Red Ensign
 * 6 June
 * Are We Civilized?
 * 8 June
 * Now I'll Tell
 * 13 June
 * The Circus Clown
 * 28 June
 * Of Human Bondage
 * The World Moves On
 * 30 June
 * Baby Take a Bow

July–September

 * July 1934
 * 6 July
 * Charlie Chan's Courage
 * 13 July
 * Kiss and Make-Up
 * The Old Fashioned Way
 * We're Rich Again
 * 20 July
 * Grand Canary
 * 21 July
 * Here Comes the Navy
 * 30 July
 * The Cat's-Paw
 * August 1934
 * 3 August
 * The Girl from Missouri
 * 4 August
 * The Man with Two Faces
 * 6 August
 * One More River
 * 13 August
 * Everybody's Woman (Italy)
 * 15 August
 * Bulldog Drummond Strikes Back
 * Jane Eyre
 * 16 August
 * Dames
 * 17 August
 * Treasure Island
 * 23 August
 * Unfinished Symphony
 * 24 August
 * Hide-Out
 * 30 August
 * Crime Without Passion
 * 31 August
 * Chained
 * Now and Forever
 * Peck's Bad Boy
 * She Loves Me Not
 * September 1934
 * 5 September
 * One Night of Love
 * 7 September
 * The Count of Monte Cristo
 * 11 September
 * Maniac
 * 12 September
 * L'Atalante (France)
 * Charlie Chan in London
 * 14 September
 * The Barretts of Wimpole Street
 * Death on the Diamond
 * 15 September
 * The Scarlet Empress
 * 17 September
 * Young and Beautiful
 * 19 September
 * A Lost Lady
 * 21 September
 * Belle of the Nineties
 * The Richest Girl in the World
 * 22 September
 * The Case of the Howling Dog
 * 28 September
 * Judge Priest
 * The Pursuit of Happiness

October–December

 * October 1934
 * 1 October
 * She Had to Choose
 * 2 October
 * Our Daily Bread
 * 4 October
 * Jew Süss
 * 5 October
 * Cleopatra
 * 8 October
 * The Return of Bulldog Drummond
 * 13 October
 * Madame Du Barry
 * 18 October
 * Man of Aran (GB)
 * 19 October
 * Forbidden Territory
 * The Gay Divorcee
 * What Every Woman Knows
 * 22 October
 * The Captain Hates the Sea
 * Great Expectations
 * The Trail Beyond
 * November 1934
 * 2 November
 * The Merry Widow(France/US)
 * 3 November
 * Gambling
 * 9 November
 * Evelyn Prentice
 * 10 November
 * Kid Millions
 * The St. Louis Kid
 * 16 November
 * The White Parade
 * 17 November
 * Girl o' My Dreams
 * It's a Gift
 * 23 November
 * Anne of Green Gables
 * The Painted Veil
 * 26 November
 * Imitation of Life
 * 29 November
 * Road House(GB)
 * 30 November
 * Babes in Toyland
 * Broadway Bill
 * The Iron Duke
 * The Private Life of Don Juan (GB)
 * December 1934
 * 1 December
 * Flirtation Walk
 * 7 December
 * A Wicked Woman
 * 9 December
 * Lieutenant Kijé
 * 10 December
 * Something Always Happens (GB)
 * 11 December
 * Limehouse Blues
 * Le Roi des Champs-Élysées (France)
 * 14 December
 * The Dream Car
 * The Gay Bride
 * 21 December
 * The Silver Streak
 * 23 December
 * Forsaking All Others
 * The Mighty Barnum
 * The Scarlet Pimpernel (GB)
 * 28 December
 * Bright Eyes
 * Here is My Heart
 * The Little Minister
 * 31 December
 * Evergreen (GB)

Notable films released in 1934
United States unless stated

0-9

 * 1860 – (Italy)

A

 * All of Me, starring Miriam Hopkins and Fredric March
 * Amok, directed by Fedor Ozep – (France)
 * Angèle, directed by Marcel Pagnol, starring Fernandel – (France)
 * Anne of Green Gables, starring Anne Shirley
 * Are We Civilized?, starring William Farnum
 * L'Atalante, directed by Jean Vigo, starring Michel Simon – (France)

B

 * Babes in Toyland, starring Laurel and Hardy
 * Baby, Take a Bow, starring Shirley Temple
 * The Barretts of Wimpole Street, starring Norma Shearer, Fredric March and Charles Laughton
 * The Battle, starring Merle Oberon, Charles Boyer and John Loder – (GB/France)
 * Belle of the Nineties, starring Mae West and Johnny Mack Brown
 * The Big Road (Dalu), directed by Sun Yu – (China)
 * The Big Shakedown, starring Bette Davis and Charles Farrell
 * The Black Cat, starring Boris Karloff and Bela Lugosi
 * Bolero, starring George Raft and Carole Lombard
 * Boots! Boots!, starring George Formby – (GB – first film by Blakeley's Productions)
 * Born to Be Bad, starring Cary Grant, Loretta Young, Jackie Kelk
 * Bright Eyes, starring Shirley Temple
 * Broadway Bill, directed by Frank Capra, starring Warner Baxter and Myrna Loy
 * Bulldog Drummond Strikes Back, starring Ronald Colman

C

 * The Captain Hates the Sea, starring Victor McLaglen and John Gilbert in his last film role
 * Carolina, starring Janet Gaynor and Lionel Barrymore
 * The Case of the Howling Dog, starring Warren William (as Perry Mason)
 * The Cat and the Fiddle, starring Ramón Novarro and Jeanette MacDonald
 * The Cat's-Paw, starring Harold Lloyd
 * Chained, starring Joan Crawford and Clark Gable
 * Chapayev – winner of National Board of Review "Best Foreign Film" Award in 1935 – (U.S.S.R.)
 * Charlie Chan in London, starring Warner Oland and Ray Milland
 * Charlie Chan's Courage, starring Warner Oland
 * The Circus Clown, starring Joe E. Brown
 * City Limits
 * Cleopatra, directed by Cecil B. DeMille, starring Claudette Colbert and Warren William
 * Colonel Blood, starring Frank Cellier
 * The Count of Monte Cristo, starring Robert Donat
 * Crime Without Passion, starring Claude Rains

D

 * Dames, choreographed by Busby Berkeley, starring Joan Blondell, Dick Powell and Ruby Keeler
 * David Harum starring Will Rogers
 * Dark Hazard, starring Edward G. Robinson
 * Death on the Diamond, starring Robert Young
 * Death Takes a Holiday, starring Fredric March
 * The Dream Car (Meseautó), directed by Béla Gaál and starring Zita Perczel, Ella Gombaszögi and Klári Tolnay – (Hungary)
 * Don't Make Grandpa Angry (Nezlobte dědečka), directed by Karel Lamač, starring Vlasta Burian, Čeněk Šlégl and Adina Mandlová – (Czechoslovakia)

E

 * Evelyn Prentice, starring William Powell and Myrna Loy
 * Evergreen, directed by Victor Saville, starring Jessie Matthews – (GB)
 * Everybody's Woman (La signora di tutti), directed by Max Ophüls, starring Isa Miranda – (Italy)

F

 * Fashions of 1934, starring William Powell and Bette Davis
 * Ferdowsi, starring Abdolhossein Sepanta and Ardeshir Irani (Iran)
 * Frontier Marshal, starring George O' Brien
 * Fog Over Frisco, starring Bette Davis
 * Forbidden Territory, starring Gregory Ratoff, Ronald Squire, Binnie Barnes – (GB)
 * Forsaking All Others, starring Joan Crawford, Clark Gable and Robert Montgomery

G

 * Gambling, starring George M. Cohan
 * Gambling Lady, starring Barbara Stanwyck
 * The Gay Bride, starring Carole Lombard
 * The Gay Divorcee, starring Fred Astaire and Ginger Rogers
 * The Girl from Missouri, starring Jean Harlow
 * Girl o' My Dreams, starring Mary Carlisle, Edward J. Nugent, Lon Chaney Jr., Sterling Holloway
 * Glamour, starring Paul Lukas
 * The Goddess (Shen nu) – (China)
 * Grand Canary, starring Warner Baxter
 * Le Grand Jeu (The Great Game), directed by Jacques Feyder – (France)
 * Great Expectations, starring Henry Hull and Jane Wyatt

H

 * Here Comes the Navy, starring James Cagney and Pat O'Brien
 * Here is My Heart, starring Bing Crosby and Kitty Carlisle
 * Hide-Out, starring Robert Montgomery and Margaret Sullavan
 * Hollywood Party, starring Stan Laurel, Oliver Hardy, Jimmy Durante and Lupe Vélez
 * The House of Rothschild, starring George Arliss and Loretta Young

I

 * I've Got Your Number, starring Joan Blondell and Pat O'Brien
 * Imitation of Life, starring Claudette Colbert and Warren William
 * The Iron Duke, starring George Arliss
 * It Happened One Night, directed by Frank Capra, starring Clark Gable and Claudette Colbert – winner of 5 Academy Awards
 * It's a Gift, starring W. C. Fields

J

 * Jane Eyre, starring Virginia Bruce and Colin Clive
 * Jew Suss, starring Conrad Veidt
 * Jimmy the Gent, starring James Cagney and Bette Davis
 * Jolly Fellows (Vesyolye rebyata) – the first Russian musical
 * Juárez y Maximiliano (Juarez and Maximilian) – (Mexico)
 * Judge Priest, starring Will Rogers

K

 * The Key, starring William Powell and Edna Best
 * Kid Millions, starring Eddie Cantor
 * Kiss and Make-Up, starring Cary Grant, Helen Mack

L

 * The Lady Is Willing, starring Leslie Howard and Cedric Hardwicke – (GB)
 * The Last Round-Up, starring Randolph Scott
 * Lieutenant Kijé – (U.S.S.R.)
 * Liliom, directed by Fritz Lang, starring Charles Boyer – (France)
 * Limehouse Blues, starring George Raft and Jean Parker
 * Little Man, What Now?, starring Margaret Sullavan and Douglass Montgomery
 * The Little Minister, starring Katharine Hepburn and John Beal
 * Little Miss Marker, starring Shirley Temple
 * A Lost Lady, starring Barbara Stanwyck
 * The Lost Patrol, starring Victor McLaglen, Boris Karloff and Wallace Ford
 * The Lucky Texan, starring John Wayne

M-N

 * Madame Du Barry, starring Dolores del Río
 * The Man from Utah, starring John Wayne
 * Man of Aran (documentary), directed by Robert Flaherty – (GB)
 * The Man Who Knew Too Much, directed by Alfred Hitchcock, starring Leslie Banks, Edna Best and Peter Lorre – (GB)
 * The Man with Two Faces, starring Edward G. Robinson
 * Managed Money, starring Shirley Temple
 * Mandalay, starring Kay Francis
 * Manhattan Melodrama, starring Clark Gable, William Powell and Myrna Loy
 * Maniac, starring Horace B. Carpenter
 * Mauvaise Graine, directed by Billy Wilder – (FR)
 * The Merry Widow (La veuve joyeuse), directed by Ernst Lubitsch, starring Maurice Chevalier and Jeanette MacDonald – (France/US)
 * Les Misérables, directed by Raymond Bernard, starring Harry Baur and Charles Vanel – (France)
 * The Mighty Barnum, starring Wallace Beery
 * Murder at Monte Carlo, starring Errol Flynn – (GB)
 * Now and Forever, starring Gary Cooper and Carole Lombard
 * Now I'll Tell, starring Spencer Tracy

O

 * Of Human Bondage, starring Leslie Howard and Bette Davis
 * The Old Curiosity Shop, directed by Thomas Bentley – (GB)
 * The Old Fashioned Way, starring W. C. Fields
 * One More River, directed by James Whale
 * One Night of Love, starring Grace Moore
 * Operator 13, starring Marion Davies and Gary Cooper
 * Our Daily Bread, directed by King Vidor, starring Karen Morley and Tom Keene

P

 * The Painted Veil, starring Greta Garbo and Herbert Marshall
 * Pardon My Pups, a Shirley Temple short
 * Peck's Bad Boy, directed by Edward F. Cline, starring Jackie Cooper
 * Plunder of Peach and Plum (Taoli Jie) – (China)
 * The Private Life of Don Juan, directed by Alexander Korda, starring Douglas Fairbanks and Merle Oberon – (GB)
 * The Pursuit of Happiness, directed by Alexander Hall

R

 * Radio Parade of 1935, starring Will Hay – (GB)
 * Red Ensign, starring Leslie Banks – (GB)
 * The Return of Bulldog Drummond, starring Ralph Richardson and Ann Todd – (GB)
 * The Richest Girl in the World, starring Miriam Hopkins, Joel McCrea and Fay Wray
 * Riptide, starring Norma Shearer and Robert Montgomery
 * The Rise of Catherine the Great, starring Elisabeth Bergner and Douglas Fairbanks, Jr. – (GB)
 * Road House, directed by Maurice Elvey, starring Violet Loraine and Gordon Harker (GB)
 * Le Roi des Champs-Élysées (The King of the Champs-Élysées), starring Buster Keaton – (France)

S

 * Sadie McKee, starring Joan Crawford
 * The Scarlet Empress, directed by Josef von Sternberg, starring Marlene Dietrich and John Lodge
 * The Scarlet Pimpernel, starring Leslie Howard and Merle Oberon – (GB)
 * Servants' Entrance, starring Janet Gaynor
 * She Loves Me Not, starring Miriam Hopkins and Bing Crosby
 * Shirin and Farhad, starring Roohangiz Saminejad (Iran)
 * The Silver Streak, starring Charles Starrett
 * Sing as We Go, starring Gracie Fields and Stanley Holloway – (GB)
 * Six of a Kind, starring Charles Ruggles, Mary Boland and W. C. Fields
 * Something Always Happens, directed by Michael Powell, starring, Ian Hunter, Nance O'Neil, Peter Gawthorne, Muriel George – (GB)
 * The Song of Ceylon, documentary directed by Basil Wright – (GB)
 * Song of the Fishermen (Yu guang qu) – (China)
 * Spitfire, starring Katharine Hepburn
 * The St. Louis Kid, starring James Cagney
 * Stand Up and Cheer!, starring Warner Baxter and Madge Evans, featuring 5-year-old Shirley Temple
 * A Story of Floating Weeds (Ukikusa monogatari), directed by Yasujirō Ozu – (Japan)

T

 * The Tars – (Netherlands)
 * Tarzan and His Mate, starring Johnny Weissmuller and Maureen O'Sullivan
 * The Thin Man, directed by W. S. Van Dyke, starring William Powell and Myrna Loy
 * Thirty-Day Princess, starring Sylvia Sidney and Cary Grant
 * Those Were the Days, directed by Thomas Bentley, starring Will Hay and John Mills – (GB)
 * The Trail Beyond, starring John Wayne
 * Treasure Island, starring Wallace Beery and Jackie Cooper
 * Twentieth Century, directed by Howard Hawks, starring John Barrymore and Carole Lombard
 * Twenty Million Sweethearts, starring Pat O'Brien, Dick Powell and Ginger Rogers

U-V

 * Unfinished Symphony, directed by Anthony Asquith (GB/Austria)
 * Viva Villa!, starring Wallace Beery, Leo Carrillo and Fay Wray

W

 * Waltzes from Vienna, directed by Alfred Hitchcock, starring Esmond Knight and Jessie Matthews – (GB)
 * We're Not Dressing, starring Bing Crosby and Carole Lombard
 * We're Rich Again, starring Edna May Oliver and Billie Burke
 * What Every Woman Knows, starring Helen Hayes
 * Whirlpool, starring Jack Holt and Jean Arthur
 * The White Parade, starring Loretta Young
 * A Wicked Woman, starring Mady Christians, Jean Parker and Charles Bickford
 * The Woman of the Port (La Mujer del Puerto) – (Mexico)
 * Wonder Bar, starring Al Jolson
 * Workers, Let's Go (Hej rup!), directed by Martin Frič – (Czechoslovakia)

Y-Z

 * You Can't Buy Everything, starring May Robson and Jean Parker
 * You're Telling Me!, starring W. C. Fields
 * Young and Beautiful
 * Zouzou, directed by Marc Allégret, starring Jean Gabin and Josephine Baker – (France)

Serials

 * Burn 'Em Up Barnes (released June 16) (12-chapter Mascot Pictures action), starring Frankie Darro and (as Barnes) Jack Mulhall
 * Mystery Mountain (released December 3) (12-chapter Mascot Pictures western), starring Ken Maynard
 * The Lost Jungle
 * The Law of the Wild, starring Rin Tin Tin
 * Pirate Treasure
 * The Red Rider (released July 16) (15-chapter Universal Pictures western), starring Buck Jones
 * Tailspin Tommy (released October 29) (12-chapter Universal Pictures action), starring Maurice Murphy
 * The Vanishing Shadow
 * Young Eagles

Comedy film series and shorts

 * Harold Lloyd (1913–1938)

 * The Cat's-Paw
 * Lupino Lane (1915–1939)

 * My Old Duchess (directed by)
 * Buster Keaton (1917–1944)

 * The Gold Ghost (short, directed by)
 * Allez Oop (short, directed by)
 * Le Roi des Champs-Élysées (feature)
 * Laurel and Hardy (1921–1945)

 * Oliver the Eighth (short)
 * Hollywood Party (feature)
 * Going Bye-Bye! (short)
 * Them Thar Hills (short)
 * Babes in Toyland (feature)
 * The Live Ghost (short)
 * Our Gang (1922–1944)

 * Hi'-Neighbor!
 * For Pete's Sake!
 * The First Round-Up
 * Honky Donkey
 * Mike Fright
 * Washee Ironee
 * Harry Langdon (1924–1936)

 * Circus Hoodoo (short)
 * Petting Preferred (short)
 * Counsel on De Fence (short) as Darrow Langdon
 * Shivers (short) as Ichabod Somerset Crop
 * Wheeler & Woolsey (1929–1937)

 * Hips, Hips, Hooray!
 * Cockeyed Cavaliers
 * Kentucky Kernels
 * Ted Healy and His Stooges (1933–1934)
 * The Three Stooges (1934–1959)

 * Woman Haters (May 5)
 * Punch Drunks (July 13)
 * Men in Black (September 28) AAN
 * Screen Snapshots Series 14 #1 (September 29)
 * Screen Snapshots Series 14 #2 (October 26)
 * The Captain Hates the Sea (November 28) §
 * Three Little Pigskins (December 8)

Animated short film series

 * Krazy Kat (1925–1940)
 * The Autograph Hunter
 * Southern Exposure
 * Tom Thumb
 * Cinder Alley
 * Bowery Daze
 * Busy Bus
 * Masquerade Party
 * The Trapeze Artist
 * The Katnips of 1940
 * Krazy's Waterloo
 * Goofy Gondolas
 * Oswald the Lucky Rabbit (1927–1938)
 * Chicken Reel
 * The Candy House
 * The County Fair
 * The Toy Shoppe
 * Kings Up
 * Wolf! Wolf!
 * The Ginger Bread Boy
 * Goldielocks and the Three Bears
 * Annie Moved Away
 * Wax Works
 * William Tell
 * Chris Columbus, Jr.
 * The Dizzy Dwarf
 * Ye Happy Pilgrims
 * Sky Larks
 * Spring in the Park
 * Mickey Mouse (1928–1953)
 * Shanghaied
 * Camping Out – known as "Camping Troubles" in releases outside the United States.
 * Playful Pluto
 * Gulliver Mickey
 * Hollywood Party (guest appearance)
 * Mickey's Steam Roller – First appearance of Mickey's nephews.
 * Orphan's Benefit – First time Donald Duck from The Wise Little Hen appears in a Mickey cartoon. First appearance of Clara Cluck. Last black and white appearance of Clarabelle Cow and Horace Horsecollar. First cartoon were Mickey wears a shirt.
 * Mickey Plays Papa
 * The Dognapper
 * Babes in Toyland (guest appearance in live action; costumed character)
 * Two-Gun Mickey – Last black and white appearance of Minnie Mouse.
 * Silly Symphonies (1929–1939)
 * The China Shop
 * The Grasshopper and the Ants
 * Funny Little Bunnies
 * The Big Bad Wolf
 * The Wise Little Hen
 * The Flying Mouse
 * Peculiar Penguins
 * The Goddess of Spring
 * Screen Songs (1929–1938)
 * Keeps Rainin' All the Time
 * Let's All Sing Like the Birdies Sing
 * Tune Up and Sing
 * Lazy Bones
 * This Little Piggie Went to Market
 * She Reminds Me of You
 * Love Thy Neighbor
 * Let's Sing with Popeye
 * Looney Tunes and Merrie Melodies (1930–1969)
 * Buddy the Gob
 * Pettin' in the Park
 * Honeymoon Hotel
 * Buddy and Towser
 * Buddy's Garage
 * Beauty and the Beast
 * Those Were Wonderful Days
 * Buddy's Trolley Troubles
 * Goin' to Heaven on a Mule
 * Buddy of the Apes
 * How Do I Know It's Sunday
 * Buddy's Bearcats
 * Why Do I Dream Those Dreams
 * The Girl at the Ironing Board
 * The Miller's Daughter
 * Shake Your Powder Puff
 * Buddy the Detective
 * Rhythm in the Bow
 * Buddy the Woodsman
 * Buddy's Circus
 * Those Beautiful Dames
 * Buddy's Adventures
 * Pop Goes Your Heart
 * Viva Buddy
 * Buddy the Dentist
 * Terrytoons (1930–1964)
 * Scrappy (1931–1941)
 * Betty Boop (1932–1939)
 * She Wronged Him Right
 * Red Hot Mamma
 * Ha! Ha! Ha!
 * Betty in Blunderland
 * Betty Boop's Rise to Fame
 * Betty Boop's Trial
 * Betty Boop's Lifeguard
 * Poor Cinderella (first and only Betty Boop cartoon in colour)
 * There's Something About a Soldier
 * Betty Boop's Little Pal
 * Betty Boop's Prize Show
 * Keep in Style
 * When My Ship Comes In
 * Popeye the Sailor (1933–1957)
 * Willie Whopper (1933-1934)
 * ComiColor Cartoons (1933–1936)
 * Cubby Bear (1933-1934)
 * The Little King (1933-1934)
 * Happy Harmonies (1934–1938)
 * Cartune Classics (1934–1935)
 * Color Rhapsodies (1934–1949)
 * Amos 'n' Andy (1934)

Births

 * January 6 – Sylvia Syms, English actress (d. 2023)
 * January 8 – Roy Kinnear, British character actor (d. 1988)
 * January 11 – Mitchell Ryan, American actor (d. 2022)
 * January 14 – Richard Briers, English actor (d. 2013)
 * - Priscilla Morgan, English actress
 * January 20 – Tom Baker, British actor
 * January 21
 * Audrey Dalton, Irish actress
 * Ann Wedgeworth, American character actress (d. 2017)
 * January 22 – Bill Bixby, American actor (d. 1993)
 * January 23 – Carmine Caridi, American actor (d. 2019)
 * January 25 – Donald W. Ernst, American editor and producer (d. 2023)
 * February 5 - Jimmy Flynn, American actor (d. 2022)
 * February 10 – Tatyana Lolova, Bulgarian actress (d. 2021)
 * February 11 – Tina Louise, American actress
 * February 12
 * Annette Crosbie, Scottish actress
 * Valerio Ruggeri, Italian actor and voice actor (d. 2015)
 * February 13 – George Segal, American actor and musician (d. 2021)
 * February 14 - Florence Henderson, American actress (d. 2016)
 * February 17
 * Alan Bates, English actor (d. 2003)
 * Barry Humphries, Australian comedian, actor, satirist, artist and author (d. 2023)
 * February 21 – Rue McClanahan, American actress (d. 2010)
 * March 4 – Anne Haney, American actress (d. 2001)
 * March 5
 * James Sikking, American actor (d. 2024)
 * Nicholas Smith, English comedy actor (d. 2015)
 * March 9
 * Del Close, American actor, writer and teacher (d. 1999)
 * Joyce Van Patten, American actress
 * March 12 - Henryk Bista, Polish actor (d. 1997)
 * March 22 – May Britt, Swedish actress
 * March 26
 * Alan Arkin, American actor (d. 2023)
 * Norman Reynolds, English production designer (d. 2023)
 * March 27 – Peter Schamoni, German director (d. 2011)
 * March 30 - Count Prince Miller, British actor and musician (d. 2018)
 * March 31
 * Richard Chamberlain, American actor and singer
 * Shirley Jones, American singer and actress
 * April 1 - Don Hastings, American actor
 * April 2 – Shirley Douglas, Canadian actress (d. 2020)
 * April 4 - Helen Hanft, American actress (d. 2013)
 * April 7 – Ian Richardson, Scottish actor (d. 2007)
 * April 14 – Josef Somr, Czech actor (d. 2022)
 * April 16 – Robert Stigwood, Australian-born British producer (d. 2016)
 * April 24 – Shirley MacLaine, American actress
 * April 25 – Denny Miller, American actor (d. 2014)
 * May 1 – John Meillon, Australian character actor (d. 1989)
 * May 3 – Ivan Andonov, Bulgarian film director (d. 2011)
 * May 11 – André Gregory, French-born American director, writer and actor
 * May 18 – Dwayne Hickman, American actor, producer and director (d. 2022)
 * May 22 – Fred Roos, American film producer (d. 2024)
 * May 24 – Kiril Gospodinov, Bulgarian actor (d. 2003)
 * May 29 – Marina Cicogna, Italian producer (d. 2023)
 * June 1
 * Pat Boone, American singer and actor
 * Peter Masterson, American actor, director, producer and writer (d. 2018)
 * June 8 – Millicent Martin, English actress, singer and comedian
 * June 15
 * Eileen Atkins, British actress
 * William Newman, American actor (d. 2015)
 * June 16
 * Bill Cobbs, American actor (d. 2024)
 * Jane Henson, American puppeteer (d. 2013)
 * June 21
 * Terrence Evans, American actor (d. 2015)
 * Maro Kontou, Greek actress and politician
 * Maggie Jones, English actress (d. 2009)
 * June 26 – Josef Sommer, German-American actor
 * July 1
 * Jamie Farr, American actor
 * Jean Marsh, English actress (Upstairs, Downstairs)
 * Ester Pajusoo, Estonian actress
 * Sydney Pollack, American director, producer and actor (d. 2008)
 * July 5 – Nikolay Binev, Bulgarian actor (d. 2003)
 * July 8 – Marty Feldman, English comedian and actor (d. 1982)
 * July 10 – Jerry Nelson, American puppeteer (d. 2012)
 * July 15 – Eva Krížiková, Slovak actress (d. 2020)
 * July 22
 * Eric Del Castillo, Mexican actor
 * Louise Fletcher, American actress (d. 2022)
 * July 23 – Silvana Bosi, Italian actress (d. 2020)
 * July 26 – Ken Pogue, Canadian actor (d. 2015)
 * July 29 – Sergio Fiorentini, Italian actor and voice actor (d. 2014)
 * August 5 – Zakes Mokae, South African-American actor (d. 2009)
 * August 7 – Marija Kohn, Croatian actress (d. 2018)
 * August 14 – Vernon Dobtcheff, British actor
 * August 24 – Kenny Baker, English-born actor (d. 2016)
 * August 30 – Helen Craig, English children's author and illustrator (Angelina Ballerina)
 * September 2 - Chuck McCann, American actor, comedian, puppeteer and television host (d. 2018)
 * September 5 - Dennis Letts, American actor (d. 2008)
 * September 11 – Ian Abercrombie, English-American actor and comedian (d. 2012)
 * September 18 - Eddie Jones, American actor (d. 2019)
 * September 20
 * Sophia Loren, Italian actress
 * Jeff Morris, American actor (d. 2004)
 * Karen Sharpe, American actress
 * September 24 - Robert Lang, English actor (d. 2004)
 * September 27
 * Wilford Brimley, American actor (d. 2020)
 * Claude Jarman Jr., American child actor
 * September 28 – Brigitte Bardot, French actress
 * September 29 – Alan Hopgood, Australian actor (d. 2022)
 * October 13 – Savely Kramarov, Russian-American actor (d. 1995)
 * October 15 – Peter Haskell, American actor (d. 2010)
 * October 19 – Glória Menezes, Brazilian actress
 * October 20 – Timothy West, English actor
 * October 28 - Charles A. Gargano, Italian-American actor
 * October 31 - Suzanne Shepherd, American actress (d. 2023)
 * November 5 – Kira Muratova, Russian director (d. 2018)
 * November 10
 * Richard Bradford, American actor (d. 2016)
 * Joanna Moore, American actress (d. 1997)
 * November 11
 * Suzanne Lloyd, Canadian actress
 * Nadine Trintignant, French director, producer and screenwriter
 * November 13 – Garry Marshall, American director, actor, producer, writer and voice artist (d. 2016)
 * November 15 – Joanna Barnes, American actress (d. 2022)
 * November 21
 * Jack Kehoe, American actor (d. 2020)
 * Laurence Luckinbill, American actor, playwright and director
 * November 23 – Michael Wayne, American producer and actor (d. 2003)
 * November 25 – Ann Davies, English actress (d. 2022)
 * November 28 – Jaakko Pakkasvirta, Finnish film director and screenwriter (d. 2018)
 * December 9 – Judi Dench, English actress
 * December 16 – Pete Schrum, American actor (d. 2003)
 * December 26 – Matt Zimmerman, Canadian actor (d. 2022)
 * December 28 – Maggie Smith, English actress
 * December 29 – Forugh Farrokhzad, Iranian poet and film director (d. 1967)
 * December 30 – Russ Tamblyn, American actor

Deaths

 * March 21 – Lilyan Tashman, 34, American actress (cancer)
 * May 31 – Lew Cody, 50, American actor
 * June 8 – Dorothy Dell, 19, American actress (road accident)
 * July 6 – Harry A. Pollard, 55, American actor & director
 * July 28 – Marie Dressler, 65, Canadian-born American Academy Award winning actress (cancer)

Debuts

 * Gene Autry – In Old Santa Fe
 * Virginia Carroll – Sweet Adeline
 * Esther Dale – Crime Without Passion
 * Donald Duck – The Wise Little Hen
 * Alice Faye – George White's Scandals
 * Alec Guinness – Evensong
 * Sara Haden – Spitfire
 * Rita Hayworth – Cruz Diablo
 * Kathleen Howard – Death Takes a Holiday
 * Sam Jaffe – The Scarlet Empress
 * Margaret Lockwood – Lorna Doone
 * Louise Lorimer – I've Got Your Number
 * Keye Luke – The Painted Veil
 * Ann Miller – Anne of Green Gables
 * Anne Revere – Double Door
 * Rosalind Russell – Evelyn Prentice
 * Ann Rutherford – Student Tour
 * George Sanders – Love, Life and Laughter
 * Ann Sheridan – Search for Beauty
 * Robert Taylor – Handy Andy
 * Lurene Tuttle – Stand Up and Cheer!
 * Chill Wills – It's a Gift
 * Ian Wolfe – The Barretts of Wimpole Street
 * Jane Wyatt – One More River

title: 1934 in film