Computing superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group

Ryo Ohashi; Momonari Kudo

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arXiv · 2312.16858

Computing superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group

Ryo Ohashi·Momonari Kudo

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Abstract

In algebraic geometry, enumerating or finding superspecial curves in positive characteristic $p$ is important both in theory and in computation. In this paper, we propose feasible algorithms to enumerate or find superspecial hyperelliptic curves of genus $4$ with automorphism group properly containing the Klein $4$-group. Executing the algorithms on Magma, we succeeded in enumerating such superspecial curves for every $p$ with $19 \leq p < 500$, and in finding a single one for every $p$ with $19 \leq p < 7000$.

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BibTeX RIS

Ryo Ohashi, Momonari Kudo. 2023-12-28. Computing superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group. https://arxiv.org/abs/2312.16858

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