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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.

3 votes

Are most cubic plane curves over the rationals elliptic?

"One could try to estimate the size of the Tate-Shafarevich group of a "random" elliptic curve, to get an idea of how often local solvability implies global solvability, but even if one does this it i …
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3 votes

Class Field Theory for Imaginary Quadratic Fields

Magma is not facile here but works, but maybe SAGE can do the same. You get $K(j,E[3])/K$ to be a degree 12 and cyclic Galois group, for the $E$ I think you want. > jrel:=PowerRelation(jInvariant((1+ …
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8 votes
Accepted

Class Field Theory for Imaginary Quadratic Fields

Here is a case where it is non-Abelian. I use $K$ of class number 3. If I use the Gross curve, it is Abelian. If I twist in $Q(\sqrt{-15})$, it is Abelian for every one I tried, maybe because it is on …
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