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Computing isogenies from modular equations in genus two

Jean Kieffer 1, 2 Aurel Page 1, 2 Damien Robert 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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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Submitted on : Wednesday, October 28, 2020 - 4:29:00 PM
Last modification on : Saturday, December 4, 2021 - 3:43:58 AM

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  • HAL Id : hal-02436133, version 2
  • ARXIV : 2001.04137

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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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