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

We are searching for rank 8 elliptic curves with the torsion subgroup $\mathbb{Z}/6$ using newly discovered families similar to Kihara's as described in A. Dujella, J.C. Peral, P. Tadić, Elliptic ...
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### Z/8Z elliptic curve with a missing generator

We are searching for the rank $6$ elliptic curves with the torsion subgroup $\mathbb{Z}/8\mathbb{Z}$ using the families similar to Allan MacLeod's as described in A. J. MacLeod, A Simple Method for ...
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### Example of elliptic curve with CM (complex multiplication) by \sqrt{-7}

Can someone give me an example of elliptic curve with CM by sqrt(-7) with the action. I've found a list of examples in the following link but not the action. http://planetmath.org/...
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### congruent number problem [closed]

I am studying the congruent number problem and I heard that there is a paper by Kazuma Morita which claims to solve this problem from my colleague. I saw the paper on his homepage but it is very ...
341 views

### Argument for unboundedness of integral points of elliptic curves over number fields

Probably this is well known to those who know it. Got an argument and numerical support that over number fields elliptic curves in minimal models might have unbounded number of integral points, the ...
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### Euler Systems and Coleman’s Conjecture

I’m trying to work on Coleman’s conjecture for abelian extensions of imaginary quadratic fields. I’ve read most papers by Seo regarding circular distributions. However, I’m a still confused about what ...
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