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Results tagged with elliptic-curves
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user 30999
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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Main conjecture for elliptic curves
Suppose $E$ is an elliptic curve defined over $\mathbb{Q}$ with good ordinary reduction at a prime $p$. Then one can define nonnegative integers $ \lambda_{E}^{alg} $, $ \mu_{E}^{alg} $, $ \lambda_{E} …
- 1,949
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answer
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Finding out $p$-torsion elements of an elliptic curve $E$ over $\mathbb{Q}_p$
Let $E$ be an elliptic curve over $\mathbb{Q}$.
Then how to compute the $p$-torsion elements of $E$ over the $p$-adic field $\mathbb{Q}_p$ using SAGE or any other means ?
At least can we say whether …
- 8,945
14
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3
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Order of torsion group
What can one say about the order of the torsion group of an elliptic curve defined over the compositum of all quadratic extensions of $\mathbb{Q}$ ?
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Elliptic curves over $\mathbb{Q}$ with no rational torsion and $\mu$-invariant equal to 1 at...
How to find out examples over elliptic curves over $\mathbb{Q}$ with no rational torsion and $\mu$-invariant equal to 1 at $p=3$ $?$
- 1,680
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answer
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Some questions related to Iwasawa invariants of elliptic curves
Let $E$ be an elliptic curve defined over $\mathbb{Q}$ with good ordinary reduction at an odd prime $p$.
Let $\mathbb{Z}_{p}$ denote the ring of $p$-adic integers, and $\mathbb{Q}^{cyc}$ be the cyclo …
- 10.9k
4
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answers
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Main conjecture for elliptic curves invariant under a $\mathbb{Q}$-isogeny
Suppose $E$ is an elliptic curve defined over $\mathbb{Q}$ with good ordinary reduction at a prime $p$. Then one can define nonnegative integers $ \lambda_{E}^{alg} $, $ \mu_{E}^{alg} $, $ \lambda_{E} …
- 8,945
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Examples of elliptic curves over $\mathbb{Q}$
I need examples of two non-isogenous elliptic curves $E_{1}, E_{2}$ over $\mathbb{Q}$ having the following 2 properties -
1) $E_{1}, E_{2}$ have no rational torsion points.
2) $E_1[9] \cong E_2[9]$ …
- 13k
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answer
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Determining $\mu$-invariant of elliptic curves over $\mathbb{Q}$
From Pollack's table on his homepage, I have the values of mu invariant of elliptic curves 38B1 & 38B2 (labeled as in Cremona table). But I need to know the values of mu invariants of 38A1, 38A2, 38A3 …
- 1,209
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votes
1
answer
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$\mu$-invariant and Pontryagin dual of Selmer group of elliptic curves 2
Consider the elliptic curves -
$ E_{1}: y^{2}+y=x^{3}+x^{2}-769x-8470 $ $ [\text{Cremona}:19a2] $
$ E_{2}: y^{2}+xy+y=x^{3}-86x-2456 $ $ [\text{Cremona}:38a2] $
with both good or …
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$\mu$-invariant and Pontryagin dual of Selmer group of elliptic curves 1
1) What are the examples of elliptic curves over $\mathbb{Q}$ with good reduction and $\mu$-invariant $\geq 2$ at $p = 3$ and how to find them $?$
2) Let $\Lambda = \mathbb{Z}_{p}[[T]] $ and $ K=\ma …
- 1,209
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Supersingular elliptic curves over $\mathbb{Q}$
what are the examples of elliptic curves defined over $\mathbb{Q}$ with supersingular reduction at a prime $p$ and having a $p$-isogeny over $\mathbb{Q}$ ?
CommunityBot
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answers
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Isogeny classes and elliptic curves over finite fields
Fix a conductor and a prime $p$. Then
1) Do the elliptic curves in the same isogeny class after reduction modulo $p$ have the same number of points over the finite field $\mathbb{F}_{p} ?$
2) Do the …
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answer
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Isogeny classes and reduction types of elliptic curves at primes of bad reduction
Fix a conductor. Then
1) Do the elliptic curves in the same isogeny class have the same reduction type at a prime of bad reduction of the curve ?
2) Do the elliptic curves belonging to two differen …
- 8,945