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arXiv · 2105.13752

Constructing all Genus 2 Curves with Supersingular Jacobian

Andreas Pieper
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Abstract

L. Moret-Bailly constructed families $\mathfrak{C}\rightarrow \mathbb{P}^1$ of genus 2 curves with supersingular jacobian. In this paper we first classify the reducible fibers of a Moret-Bailly family using linear algebra over a quaternion algebra. The main result is an algorithm that exploits properties of two reducible fibers to compute a hyperelliptic model for any irreducible fiber of a Moret-Bailly family.

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Andreas Pieper. 2021-05-28. Constructing all Genus 2 Curves with Supersingular Jacobian. https://arxiv.org/abs/2105.13752

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