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Computing isogenies from modular equations in genus two

Abstract

We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2.
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Dates and versions

hal-02436133 , version 1 (12-01-2020)
hal-02436133 , version 2 (28-10-2020)

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Jean Kieffer, Aurel Page, Damien Robert. Computing isogenies from modular equations in genus two. 2020. ⟨hal-02436133v2⟩
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