Twists of non-hyperelliptic curves of genus 3

@article{Garcia2016TwistsON,
  title={Twists of non-hyperelliptic curves of genus 3},
  author={Elisa Lorenzo Garc'ia},
  journal={arXiv: Number Theory},
  year={2016}
}
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. 

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