# Questions tagged [elliptic-curves]

An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.

**153**

**2**answers

### Estimating the size of solutions of a diophantine equation

**72**

**0**answers

### The exponent of Ш of $y^2 = x^3 + px$, where $p$ is a Fermat prime

**64**

**1**answer

### Is there a "classical" proof of this $j$-value congruence?

**62**

**9**answers

### Why is an elliptic curve a group?

**61**

**3**answers

### Is there a "Basic Number Theory" for elliptic curves?

**61**

**0**answers

### Constructing non-torsion rational points (over Q) on elliptic curves of rank > 1

**43**

**5**answers

### Definition and meaning of the conductor of an elliptic curve

**38**

**1**answer

### Diophantine equation for 2016: triangular $|{\rm GL}_2({\bf F}_q)|$

**35**

**3**answers

### Is there a nice proof of the fact that there are (p-1)/24 supersingular elliptic curves in characteristic p?

**35**

**1**answer

### $x^4+y^4$ powerful for relatively prime $x,y$

**32**

**4**answers

### Why is this "the first elliptic curve in nature"?

**31**

**7**answers

### What heuristic evidence is there concerning the unboundedness or boundedness of Mordell-Weil ranks of elliptic curves over $\Bbb Q$?

**31**

**4**answers

### Is there any theory why (for Bitcoin) the discrete logarithm problem is so hard to solve?

**31**

**1**answer

### Do all curves have Néron models

**31**

**4**answers

### Over which fields does the Mordell-Weil theorem hold?

**31**

**1**answer

### Quaternionic and octonionic analogues of the Basel problem

**30**

**4**answers

### Are most cubic plane curves over the rationals elliptic?

**30**

**4**answers

### Modular curves of genus zero and normal forms for elliptic curves

**29**

**1**answer

### Modern proof of Serre's open image theorem?

**28**

**3**answers

### Elliptic curve over a scheme is a group scheme?

**28**

**2**answers

### When did people start thinking of elliptic curves as groups?

**28**

**1**answer

### Is the Modularity Theorem (currently) effective?

**27**

**0**answers

### What are the possible singular fibers of an elliptic fibration over a higher dimensional base?

**26**

**6**answers

### Does the moduli space of smooth curves of genus g contain an elliptic curve

**26**

**1**answer

### Fundamental group of the moduli stack of elliptic curves

**25**

**4**answers

### Etale cohomology and l-adic Tate modules

**25**

**6**answers

### When is a product of elliptic curves isogenous to the Jacobian of a hyperelliptic curve?

**25**

**1**answer

### Possible counterexample to a theorem assuming Lang's conjecture

**25**

**3**answers

### Can the number of solutions $xy(x-y-1)=n$ for $x,y,n \in Z$ be unbounded as n varies?

**25**

**2**answers

### How to explicitly compute lifting of points from an elliptic curve to a modular curve?

**24**

**2**answers

### Why do the $2$-Selmer ranks of $y^2 = x^3 + p^3 $ and $y^2 = x^3 - p^3 $ agree?

**24**

**1**answer

### Universal homotheties for elliptic curves

**22**

**2**answers

### unboundedness of number of integral points on elliptic curves?

**22**

**4**answers

### The class number formula, the BSD conjecture, and the Kronecker limit formula

**22**

**1**answer

### Which elliptic curves over totally real fields are modular these days?

**22**

**0**answers

### Fake CM elliptic curves

**21**

**5**answers

### Algorithms for finding rational points on an elliptic curve?

**21**

**2**answers

### State of knowledge of $a^n+b^n=c^n+d^n$ vs. $a^n+b^n+c^n=d^n+e^n+f^n$

**21**

**3**answers

### Conceptual understanding of the Gross-Zagier theorem.

**21**

**3**answers

### Consecutive square values of cubic polynomials

**21**

**2**answers

### CM $j$-invariants in $p$-adic fields

**21**

**1**answer

### The valuation of j-functions vs number of isomorphisms for an elliptic curve

**20**

**6**answers

### What are the recommended books for an introductory study of elliptic curves?

**20**

**4**answers

### Integer points of an elliptic curve

**20**

**4**answers

### Does p-adic $L$- function determine the $L$ function

**20**

**1**answer

### Cryptography and elliptic curves

**20**

**2**answers

### How can I see the relation between shtukas and the Langlands conjecture?

**20**

**1**answer

### Can one prove complex multiplication without assuming CFT?

**19**

**3**answers

### A recommended roadmap to Fermat's Last Theorem

**19**

**11**answers