# 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.

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### Pro-representability and the obstruction to deformations of “stable curve of genus one + a section”

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### Discriminant of elliptic curve (Frey-Hellegouarch), j-invariant and positive definite kernels, similarities?

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### The number of perfect squares which can occur in an arithmetic progression of length n

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### Recent developments in the proof of Fermat's last theorem

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### Conceptual explanations of the class numbers for the first few $\mathbb{Q}(\sqrt{p})$ with odd conductor

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### primes of multiplicative reduction for elliptic curves with rational $\ell$-torsion

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### Drinfeld basis of the universal formal deformation of a supersingular elliptic curve

**30**

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### Why is this “the first elliptic curve in nature”?

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### Why $E_1(\mathbb{Q}_p)\cong\mathbb{Z}_p$

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### abc triples with a symmetric condition

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### Is there a way to show that the $m$-torsion group of an elliptic curve is $(\mathbb{Z}/m\mathbb{Z})^2$ without using analytical methods?

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### Is there an infinite order $\mathbb{F}_{p}$-section for a certain elliptic surface $\mathcal{E}_n$?

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### What conditions are sufficient for two points to be independent in the Mordell-Weil group?

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### Is there a way to calculate the Picard $\mathbb{F}_q$-number of an (rational or K3) elliptic surface?

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### How I can prove or disprove that $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=1$ in rational? [duplicate]

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### properties of anti-cyclotomic extension

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### Hecke correspondence and the trace map of differential forms

**2**

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### Supersingular elliptic curves and their automorphisms

**16**

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### $3$-ranks of elliptic curves and representations $p=ax^3+by^3$

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### FLT and integral points on elliptic curves

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### Degree of morphisms and isogenies

**5**

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### reduction type of elliptic curves over $p$-adic fields and local Langlands correspondence for $GL_2(F)$

**3**

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### Family of elliptic curves in $\mathbb P^3$

**5**

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### An explicit description of $X(3)$ and its universal generalized elliptic curve

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### isogenies between elliptic curves with multiplicative reduction

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### Finding $Q(\sqrt{-2})$-rational points on $X_0(33)$

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### Finding elliptic curve with $P=[m]R$

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### Rank 3 Lagrangian vector bundles on an elliptic curve

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

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### The $S$-unit equation for functions on curves

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### Clarification: Using Hensel's Lemma to determine $K_v$-rational points on a curve

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### The Picard scheme of an ordinary singular curve

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### Perfect square quadratic expression

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### Indecomposable vector bundles on elliptic curves

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### Cubic extensions of number fields and their local nature

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### Elliptic curves and archimedean place

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### Sato-Tate for length zero intervals

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### Elliptic curves and its Neron model

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### Some questions regarding computation of the Mordell-Weil group

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### A generator needed for a Z/6 elliptic curve

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### Stacky proof of no elliptic curves over Z

**3**

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### Wiman's method for bounding the rank of an elliptic curve

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### The minimal equation of the Frey curve

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### Good reduction of finite etale covers of abelian varieties

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### Hard: One more generator needed for a Z/6 elliptic curve

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### double-and-add algorithm with(z,w)-coordinates

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### Super-singular reduction at a given prime

**7**

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### Around the diophantine equation $\frac{a}{2b+3c}+\frac{b}{2c+3a}+\frac{c}{2a+3b}=\text{odd integer}$, over positive integers

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### Generate algorithmically an elliptic curve with its exact class group structure?

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