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arXiv · 2102.08018

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

Elie Eid
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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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Elie Eid. 2021-02-16. Computing isogenies between jacobians of hyperelliptic curves of arbitrary genus via differential equations. https://arxiv.org/abs/2102.08018

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