Some genus 3 curves with many points, by Roland Auer and Jaap Top
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.
Roland Auer and Jaap Top <firstname.lastname@example.org email@example.com>