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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.

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When is a product of elliptic curves isogenous to the Jacobian of a hyperelliptic curve?

In two papers dated 2014 and 2016 (i.e., after 6 years the question was posted), this question was completely solved in genus 2 case by E. Kani. As Francesco Polizzi mentioned, this question was parti …
Harun Kir's user avatar