Some genus 3 curves with many points

Details Some genus 3 curves with many points Some genus 3 curves with many points

2002-01-16

arxiv.org/abs/math/0201320v1

Mathematics

Number Theory

Scientific paper

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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