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arXiv · 2412.03071

Generalised Howe curves of genus five attaining the Serre bound

Motoko Qiu Kawakita
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Abstract

We find that non-hyperelliptic generalised Howe curves and their twists of genus 5 attain the Hasse-Weil-Serre bound over some finite fields of order p, p^2 or p^3 for a prime p. We are able to decompose their Jacobians completely under certain assumptions and to determine the precise condition on the finite field over which they attain the Hasse-Weil-Serre bound.

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Motoko Qiu Kawakita. 2024-12-04. Generalised Howe curves of genus five attaining the Serre bound. https://arxiv.org/abs/2412.03071

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