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arXiv · 2112.11152

On the maximality of hyperelliptic Howe curves of genus 3

Ryo Ohashi
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Abstract

In this paper, we study a Howe curve $C$ in positive characteristic $p \geq 3$ which is of genus 3 and is hyperelliptic. We will show that if $C$ is superspecial, then its standard form is maximal or minimal over $\mathbb{F}_{p^2}$ without taking its $\mathbb{F}_{p^2}$-form.

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Ryo Ohashi. 2021-12-21. On the maximality of hyperelliptic Howe curves of genus 3. https://arxiv.org/abs/2112.11152

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