Computer search for curves with many points among abelian covers of genus 2 curves
Number Theory
2014-03-12 v1
Abstract
Using class field theory one associates to each curve C over a finite field, and each subgroup G of its divisor class group, unramified abelian covers of C whose genus is determined by the index of G. By listing class groups of curves of small genus one may get examples of curves with many points; we do this for all curves of genus 2 over the fields of cardinality 5,7,9,11,13 and 16, giving new entries for the tables of curves with many points (www.manYPoints.org).
Cite
@article{arxiv.1106.5176,
title = {Computer search for curves with many points among abelian covers of genus 2 curves},
author = {Karl Rökaeus},
journal= {arXiv preprint arXiv:1106.5176},
year = {2014}
}