Twists of non-hyperelliptic curves of genus 3

2016/04/08 by García, Elisa Lorenzo
#11G99 #14H10 #14H45 #14H50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1604.02410

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 non-hyperelliptic 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 non-trivial automorphism group up to C-isomorphism.

Related

• Non hyperelliptic curves of genus three over finite fields of characteristic two
• Twists of non-hyperelliptic curves
• Plane quartic twists of X(5,3)
• The a-numbers of non-hyperelliptic curves of genus 3 with cyclic automorphism group of order 6
• Classification of genus 3 curves in special strata of the moduli space