On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain $(\mathbb{Z}/2\mathbb{Z})^3$

Ryo Ohashi; Momonari Kudo

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arXiv · 2603.21569

On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain $(\mathbb{Z}/2\mathbb{Z})^3$

Ryo Ohashi·Momonari Kudo

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Abstract

While the numbers of superspecial curves of genus at most 3 are well understood, and several computational approaches have been developed to count superspecial curves of genus 4 with large automorphism groups, much less is known in higher genera. In this paper, we construct a feasible algorithm to enumerate superspecial hyperelliptic curves of genus 5 whose automorphism groups contain $(\mathbb{Z}/2\mathbb{Z})^3$. We implement and executing our algorithm in Magma, we succeeded in enumerating such superspecial curves in every characteristic $11 < p < 1000$.

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Ryo Ohashi, Momonari Kudo. 2026-03-23. On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain $(\mathbb{Z}/2\mathbb{Z})^3$. https://arxiv.org/abs/2603.21569

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