Twists of non-hyperelliptic curves of genus 3

Elisa Lorenzo García

Published 2016-04-08Version 1

In this paper we explicitly compute equations for the twists of all the smooth plane quartic curves de?fined 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.