Twists of Elliptic Curves

[摘要] In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set $H^1\big(\operatorname{G}_{\overline{K}/K}, \operatorname{Aut}_{\overline{K}}(E)\big)$. The results are illustrated by examples.

[关键词] elliptic curve;twist;automorphisms;Galois cohomology