# 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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### Factoring integers of the form $n=p q^2$ using elliptic curves

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### Torsion points on $E/\mathbb{Q}$ with large coordinates

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### Common prime of the finite number of order of imaginary quadratic field

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### Trace map on rational points of elliptic curves

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### An invariant subspace under $G_Q$ action , and BSD-rank

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### Explicit natural correspondence between cusps of $X(N)$ and isomorphism classes of level $N$ structures on Tate($q^N$)

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### Combinations of rank and torsion attainable by $E/\mathbb{Q}$

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### Finite quotients of the absolute Galois group of $\mathbb{Q}$ via torsion of elliptic curves

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### Goldfeld resolution of the quadratic class number problem

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### Z2xZ6 elliptic curves with missing generators

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### What's the average order of the reduction of a section of an elliptic curve

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### How to prove there are exactly $8$ integer points on the elliptic curve $y^2 = x^3 + 17$ [duplicate]

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### Jacobians $\mathbb{F}_q$-isogenous to the direct square of an ordinary elliptic $\mathbb{F}_q$-curve of $j$-invariant $0$

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### Analytic function with q- difference equation involving theta

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### Universal bundles over algebraic stacks

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### Frobenius actions on de Rham cohomology of ordinary elliptic curves

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### Mordell–Weil rank of some elliptic $K3$ surface

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### Elliptic curves of high rank over Quadratic extensions

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### Splitting of small primes in number fields generated by the torsion of elliptic curves

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### A subgroup of the $n$-Selmer group

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### 3-, 6-, 12-descent for Z2xZ6 elliptic curves

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### Find basis for the set of torsion points E[m]

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### The name of the equianharmonic curve

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### An explicit equation for $X_1(13)$ and a computation using MAGMA

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### Moduli interpretation and Ogg's notation for the cusps on modular curves

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### Is the reduction of an absolutely irreducible plane curve still irreducible except for the finite number of cases?

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### Elkies' theorem on supersingular primes and inertness

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### Status of $x^3+y^3+z^3=6xyz$

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### Z/8Z elliptic curve with a missing generator

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### Finding rational points via birational map

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### What upper bounds on $\sum_{n<x}a_n$ are known where $L(E,s)=\sum_{n=1}^{\infty}\frac{a_n}{n^s}$ is an Elliptic L Function?

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### What heuristic suggest for the number of solutions of $x^n+y^n=A$?

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### Monodromy Representation on $H_1$ of Elliptic Curve

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### Are there upper bounds on the L function $|L(E,s)|$ for $|s|<C$?

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### Summation form of the Hasse-Weil zeta function?

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### Understanding the implementation of the $p$-adic(?) sigma function in SageMath

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### What effect do Torsion points have on an Elliptic Curve's L function?

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### What is the minimal model of $E:y^2=x^3-x-n$?

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### Higher order inflection points

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### Distribution of the rank of $y^2=x^4+x+b^2$

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### Number of integer solutions to a system of Diophantine inequalities

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### Kihara-like Z/6Z elliptic curve families

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### Ramification index and additive reduction of elliptic curves

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### Is every sufficiently general monic quartic rational square infinitely often?

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### how often can a fixed prime be anomalous?

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### A new simple formula is needed

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### Given a point $P$ on a genus-$1$ curve over $\mathbb{Q}_p$, is there an $R$ such that $2 \mid [P - R]$ and $x(\overline{P}) \neq x(\overline{R})$?

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### Action of the symmetric group $S_3$ on an elliptic curve $E$ defined over $\mathbb{Z}$

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### Rank of jacobians of twists of hyperelliptic curves of genus one

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