Twists of nonhyperelliptic curves of genus 3
Abstract
In this paper we explicitly compute equations for the twists of all the smooth plane quartic curves defined over a number field k. Since the plane quartic curves are nonhyperelliptic curves of genus 3 we can apply the method developed by the author in a previous article. The starting point is a classification due to Henn of the plane quartic curves with nontrivial automorphism group up to Cisomorphism.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1604.02410
 Bibcode:
 2016arXiv160402410G
 Keywords:

 Mathematics  Number Theory;
 11G99;
 14H10;
 14H45;
 14H50