Twists of non-hyperelliptic 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 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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Contributor : Marie-Annick Guillemer <>
Submitted on : Thursday, October 19, 2017 - 11:51:16 AM
Last modification on : Friday, November 16, 2018 - 1:25:16 AM

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Elisa Lorenzo García. Twists of non-hyperelliptic curves of genus 3. International Journal of Number Theory, World Scientific Publishing, 2018, 14 (6), pp.1785-1812. ⟨10.1142/S1793042118501075⟩. ⟨hal-01619330⟩



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