Computer search for curves with many points among abelian covers of genus 2 curves

Details Computer search for curves with many points among abelian covers of genus 2 curves Computer search for curves with many points among abelian covers of genus 2 curves

2011-06-25

arxiv.org/abs/1106.5176v1

Mathematics

Number Theory

Scientific paper

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).

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