Vol. 302, No. 2, 2019

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Torsion of rational elliptic curves over the maximal abelian extension of $\mathbb Q$

Michael Chou

Vol. 302 (2019), No. 2, 481–509
Abstract

Let E be an elliptic curve defined over , and let ab be the maximal abelian extension of . In this article we classify the groups that can arise as E(ab)tors up to isomorphism. The method illustrates techniques for finding explicit models of modular curves of mixed level structure. Moreover, we provide an explicit algorithm to compute E(ab)tors for any elliptic curve E.

Keywords
elliptic curves, torsion, abelian, extension
Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 14H52
Milestones
Received: 12 April 2018
Revised: 4 January 2019
Accepted: 20 January 2019
Published: 27 November 2019
Authors
Michael Chou
Department of Mathematics
Tufts University
Medford, MA
United States