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Let $p$ be an odd prime number and be an integer coprime to $p$. We survey analgorithm for computing explicit rational representations of$(\ell,...,\ell)$-isogenies between Jacobians of hyperelliptic curves ofarbitrary 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 wellas in the genus of the curves.

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