Twists of Elliptic Curves
Copyright policy )Twists of Elliptic Curves
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.
- University of Groningen Netherlands
- Quaid-e-Awam University of Engineering, Science and Technology Pakistan
ABELIAN EXTENSIONS, automorphisms, Mathematics - Number Theory, Galois cohomology, math.NT, Positive characteristic ground fields in algebraic geometry, Elliptic curves over global fields, NUMBER-FIELDS, Varieties over finite and local fields, twist, FOS: Mathematics, Elliptic curves, Number Theory (math.NT), 11G05, elliptic curve
ABELIAN EXTENSIONS, automorphisms, Mathematics - Number Theory, Galois cohomology, math.NT, Positive characteristic ground fields in algebraic geometry, Elliptic curves over global fields, NUMBER-FIELDS, Varieties over finite and local fields, twist, FOS: Mathematics, Elliptic curves, Number Theory (math.NT), 11G05, elliptic curve
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