Isogenous elliptic subcovers of genus two curves

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Date

2017-11-02

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Abstract

We prove that for $N=2,3, 5, 7$ there are only finitely many genus two curves $\X$ (up to isomorphism) defined over $\Q$ with $(2, 2)$-split Jacobian and $\Aut (\X)\iso V_4$, such that their elliptic subcovers are $N$-isogenous. Also, there are only finitely many genus two curves $\X$ (up to isomorphism) defined over $\Q$ with $(3, 3)$-split Jacobian such that their elliptic subcovers are $5$-isogenous.

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Keywords

Isogeny, Cryptography

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