Vol. 302, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 332: 1  2
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
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