# 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.

**1**

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### Characterization of an Abelian surface

**5**

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### Elliptic curves and localizations at various primes

**5**

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### Magic hourglass of squares hyperelliptic equation

**5**

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### Embedding torsors of elliptic curves into projective space

**3**

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### What do congruences between modular forms tell us about $\mu$-invariants of elliptic curves?

**0**

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### Representations of elliptic curves over arbitrary fields

**3**

**1**answer

### The real part of the period of an elliptic curve

**5**

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### Do you know explicit examples of superelliptic curves $y^{\ell} = g(x)$ (for some prime $\ell > 3$) covering some elliptic curves?

**4**

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### How do you compute modular symbols?

**1**

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### To justify the intuition about #$E(\Bbb Q_p)$＝$∞$

**13**

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### Does every non-isotrivial 1-parameter family of elliptic curves have a positive rank specialization?

**6**

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### Questions on the $j$-invariant

**5**

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### Mistake in Silverman's book in proof of Neron-Ogg-Shafarevich criterion?

**0**

**0**answers

### Outline of the proof that Tamagawa number, $[E (K): E_0 (K)]$ is finite

**2**

**1**answer

### Does the modular form associated to cubic twist of a elliptic curve $E$ corresponds to some twist of $f_E$?

**4**

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### Clarification of argument in "Elliptic curves over $\mathbb{Q}_{\infty}$ are modular"

**1**

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### The existence of two $p$-isogenies implies the existence of one $p^2$-cyclic isogeny

**1**

**1**answer

### A closed subgroup $G$ of $\operatorname{GL}_2 \mathbb{Z}_\ell$ which surjects onto $\operatorname{GL}_2 \mathbb{F}_\ell$

**2**

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### Splitting of prime and order of reduction of point of infinite order in an abelian variety

**1**

**0**answers

### Brauer-Manin obstruction and affine curves

**1**

**1**answer

### Coefficients of elliptic curves over function fields

**5**

**1**answer

### Weak Mordell-Weil for EC using Chevalley-Weil theorem

**7**

**2**answers

### Supersingular curves over $\mathbb{F}_q$ and the splitting of $p$

**1**

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### A specific Diophantine equation related to the congruent number question

**-1**

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### Sum of Legendre Symbol when $p\equiv 1,3\mod{4}$

**3**

**1**answer

### An example of Serre on the cohomology of some CM elliptic curves

**0**

**1**answer

### Primes of the form $p=u^2+1$ and number of points on the elliptic curve $x^3+a x z^2=y^2 z$

**1**

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### Showing that two families of elliptic curves are diffeomorphic

**3**

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### Making Virasoro uniformization explicit for elliptic curves

**2**

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### Determining existence of a $p$-isogeny from $p|E(\mathbb{F}_{\ell})$

**1**

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### Elliptic fibrations on some Kummer surface in characteristic $2$

**3**

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### A uniform version of Bashmakov's theorem for elliptic curves

**2**

**2**answers

### Algorithm for finding integral points $P,n P$ on an elliptic curve

**3**

**1**answer

### Geometric line bundles on the Tate curve

**2**

**1**answer

### Better way to compute elliptic curves over finite fields?

**7**

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### Simultaneous reductions of elliptic curves: same number of points $|E(\Bbb F_p)| = |E'(\Bbb F_p)|$ for some prime $p$?

**2**

**0**answers

### Are there non-trivial $\mathbb{F}_q$-covers of the j-invariant 0 elliptic curve by a hyperelliptic or cyclic trigonal curve?

**5**

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### 2-descent on elliptic curves, and units modulo squares of units

**1**

**1**answer

### To integrate elliptic integral, we glue two Riemann surface to make torus

**3**

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### Mirror partners of some Calabi-Yau threefolds

**1**

**2**answers

### On the equation $x^3 + y^3 =cz^3$

**2**

**1**answer

### Where does this clever choice of differential come from? (calculating $\mathrm{H}^1_{\mathrm{dR}}(E/k))$

**2**

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

**4**

**1**answer

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

**1**

**1**answer

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

**3**

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### Trace map on rational points of elliptic curves

**0**

**0**answers

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

**3**

**1**answer

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

**3**

**1**answer

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

**2**

**1**answer