Abstract
In this paper, we compute explicit equations for the twists of all the smooth plane quartic curves defined over a number field [Formula: see text]. Since the plane quartic curves are non-hyperelliptic curves of genus [Formula: see text] we can apply the method developed by the author in a previous paper. The starting point is a classification due to Henn of the plane quartic curves with non-trivial automorphism group up to [Formula: see text]-isomorphism.
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