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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 083, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.083 (Mi sigma1283) 		 
Twists of Elliptic Curves

Max Kronberga, Muhammad Afzal Soomrob, Jaap Topa

a Johan Bernoulli Institute for Mathematics and Computer Science, Nijenborgh 9, 9747 AG Groningen, The Netherlands
b Quaid-e-Awam University of Engineering, Science & Technology (QUEST), Sakrand Road, Nawabshah, Sindh, Pakistan
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DOI: https://doi.org/10.3842/SIGMA.2017.083
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 $H^1\big(\operatorname{G}_{\overline{K}/K}, \operatorname{Aut}_{\overline{K}}(E)\big)$. The results are illustrated by examples.
Keywords: elliptic curve; twist; automorphisms; Galois cohomology.
Received: July 10, 2017; in final form October 23, 2017; Published online October 25, 2017
Bibliographic databases:
Document Type: Article
MSC: 11G05; 11G25; 14G17
Language: English
Citation: Max Kronberg, Muhammad Afzal Soomro, Jaap Top, “Twists of Elliptic Curves”, SIGMA, 13 (2017), 083, 13 pp.
Citation in format AMSBIB
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