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# On the quaternion $\ell$-isogeny path problem

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Abstract

Let $\cO$ be a maximal order in a definite quaternion algebra over $\mathbb{Q}$ of prime discriminant $p$, and $\ell$ a small prime. We describe a probabilistic algorithm, which for a given left $O$-ideal, computes a representative in its left ideal class of $\ell$-power norm. In practice the algorithm is efficient, and subject to heuri...More

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Author
David Kohel
Kristin Lauter
Christophe Petit