Papers › Constructing all Genus 2 Curves with Supersingular Jacobian
Constructing all Genus 2 Curves with Supersingular Jacobian
Andreas Pieper
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L. Moret-Bailly constructed families ℭ→ℙ¹ 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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