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Abstract
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Let
be an elliptic
curve defined over
, and
let
be the maximal
abelian extension of
.
In this article we classify the groups that can arise as
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
for any
elliptic curve
.
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Keywords
elliptic curves, torsion, abelian, extension
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Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 14H52
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Milestones
Received: 12 April 2018
Revised: 4 January 2019
Accepted: 20 January 2019
Published: 27 November 2019
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