标题： 三次非双有理曲线的扭变 显示英文标题

标题： Twists of non-hyperelliptic curves of genus 3

摘要： 在本文中，我们显式计算了定义在数域k上的所有光滑平面四次曲线的扭方程。由于平面四次曲线是非双椭圆的3亏格曲线，我们可以应用作者在之前文章中开发的方法。 起点是Henn对至多C同构的具有非平凡自同构群的平面四次曲线的分类。 显示英文摘要

摘要： 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.