Torsion of rational elliptic curves over the maximal abelian extension of ℚ

Let $E$ be an elliptic curve defined over $ℚ$ , and let $ℚ^{ab}$ be the maximal abelian extension of $ℚ$ . In this article we classify the groups that can arise as $E {(ℚ^{ab})}_{tors}$ 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 $E {(ℚ^{ab})}_{tors}$ for any elliptic curve $E ∕ ℚ$ .

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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

Vol. 302, No. 2, 2019

Michael Chou

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors