Abelian surfaces of small conductor from genus 3 double covers

Raymond van Bommel; Céline Maistret; Jia Shi; Andrew V. Sutherland

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arXiv · 2606.09512

Abelian surfaces of small conductor from genus 3 double covers

Raymond van Bommel·Céline Maistret·Jia Shi·Andrew V. Sutherland

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Abstract

We describe the construction of a database of roughly half a million abelian surfaces over Q of small conductor arising as Pryms associated to a genus 3 double cover of a genus 1 curve. Our construction uses a method that provides a degree of control over the primes of bad reduction.

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Raymond van Bommel, Céline Maistret, Jia Shi, Andrew V. Sutherland. 2026-06-08. Abelian surfaces of small conductor from genus 3 double covers. https://arxiv.org/abs/2606.09512

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