Twists of Elliptic Curves

Max Kronberg ; Muhammad Afzal Soomro ; Jaap Top

Symmetry, integrability and geometry: methods and applications, Tome 13 (2017)

Résumé

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.

Détail

Keywords: elliptic curve; twist; automorphisms; Galois cohomology.

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