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Wiman’s and Edge’s sextics attaining Serre’s bound

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We find new explicit algebraic curves of genus 6 over the finite fields \(\mathbb {F}_{67^3},\mathbb {F}_{5393}\) and \(\mathbb {F}_{9173}\) attaining Serre’s bound. They are Wiman’s and Edge’s sextics. Also we obtain a condition on p for Wiman’s sextic over the finite field \(\mathbb {F}_{p^2}\) to be maximal, and give new entries of genus 6 in the tables at manYPoints.org by computer search on Edge’s sextics.

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Acknowledgements

The author would like to express her appreciation to Shinji Miura for discussion, and the authors of KASH/KANT. This work was supported by JST PRESTO program.

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  1. Department of Mathematics, Shiga University of Medical Science, Seta Tsukinowa-cho, Otsu, Shiga, 520-2192, Japan

    Motoko Qiu Kawakita

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  1. Motoko Qiu Kawakita
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Correspondence to Motoko Qiu Kawakita.

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Kawakita, M.Q. Wiman’s and Edge’s sextics attaining Serre’s bound. European Journal of Mathematics 4, 330–334 (2018). https://doi.org/10.1007/s40879-017-0147-3

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