English

Twists of Elliptic Curves

Number Theory 2017-10-26 v3

Abstract

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 H1(GK/K,AutK(E))H^1\big(\operatorname{G}_{\overline{K}/K}, \operatorname{Aut}_{\overline{K}}(E)\big). The results are illustrated by examples.

Keywords

Cite

@article{arxiv.1707.02893,
  title  = {Twists of Elliptic Curves},
  author = {Max Kronberg and Muhammad Afzal Soomro and Jaap Top},
  journal= {arXiv preprint arXiv:1707.02893},
  year   = {2017}
}