Some genus 3 curves with many points
Number Theory
2007-05-23 v1
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.
Cite
@article{arxiv.math/0201320,
title = {Some genus 3 curves with many points},
author = {Roland Auer and Jaap Top},
journal= {arXiv preprint arXiv:math/0201320},
year = {2007}
}