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Results tagged with elliptic-curves
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user 143969
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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The minimal equation of the Frey curve
In the paper of G.Frey there is a link between stable elliptic curves and certain Diophantine equations. The Frey curve of the equation $A-B=C$ is
$$E :\;y^2=x(x-A)(x-B)$$
where $A=a^p$, $B=b^p$, …
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Inside the construction of the Frey curve
Consider the frey curve $E\mathrel: y^2=x(x-a^{p})(x+b^{p})$ with conductor $N =2\prod_{p|(abc)^{2p}}p $. Frey assume that $p$ does not divide $(abc)^{2p} $ so the level of the cusp form predict by …
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