Curves of Genus 3 with a Group of Automorphisms Isomorphic to S3

  • Jean-François Mestre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


In this talk, we construct curves of genus 3 with automorphism group equal to S3; we give some applications of this construction to the problem of optimal curves, i.e. of curves over a finite field \(\mathbb{F}_q\) having a number of points equal to the Serre-Weil bound M q ; in particular, we prove that there exists infinitely many fields \(\mathbb{F}_{3^n}\) having optimal curves; we prove also that there exists an integer C such that, for any finite field \(\mathbb{F}_{7^n}\), there exists a curve of genus 3 defined over having at least M q  − C points.

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jean-François Mestre
    • 1
  1. 1.Centre de Mathématiques de Jussieu Projet Théorie des Nombres 

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