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Some genus 3 curves with many points

Roland Auer·Jaap Top
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Abstract

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves.

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Roland Auer, Jaap Top. 2002-01-16. Some genus 3 curves with many points. https://arxiv.org/abs/math/0201320

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