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Preprints, Working Papers, ... Year : 2021

Computing isogenies between Jacobians of hyperelliptic curves of arbitrary genus via differential equations

Abstract

Let $p$ be an odd prime number and be an integer coprime to $p$. We survey an algorithm for computing explicit rational representations of $(\ell,...,\ell)$-isogenies between Jacobians of hyperelliptic curves of arbitrary genus over an extension $K$ of the field of $p$-adic numbers $\mathbb{Q}_p$. The algorithm has a quasi-linear complexity in $\ell$ as well as in the genus of the curves.
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Dates and versions

hal-03142205 , version 1 (15-02-2021)

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Elie Eid. Computing isogenies between Jacobians of hyperelliptic curves of arbitrary genus via differential equations. 2021. ⟨hal-03142205⟩
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