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Twists of Elliptic Curves

2017/07/31 by Max Kronberg, Muhammad Afzal Soomro, Jaap Top
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Cohomology #Computer science #Cryptography and Residue Arithmetic #Elliptic curve #Galois cohomology #Galois group #Galois module #Mathematics #Modular elliptic curve #Polynomial and algebraic computation #Pure mathematics #Quarter period #Schoof's algorithm #Set (abstract data type) #Supersingular elliptic curve #Twists of curves #math.NT #msc:11G05

paper · pdf · doi:10.3842/sigma.2017.083

published as SIGMA 13 (2017), 083, 13 pages

arxiv created 2017/10/25 · openalex publication_date 2017/10/25 · arxiv updated 2017/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 G K/K , Aut K (E) . The results are illustrated by examples.

Citations

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