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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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High rank elliptic curves with torsion group $\mathbb {Z}/(2\mathbb {Z})$
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by Julián Aguirre, Fernando Castañeda and Juan Carlos Peral;
Math. Comp. 73 (2004), 323-331
DOI: https://doi.org/10.1090/S0025-5718-03-01547-3
Published electronically: May 30, 2003

Abstract:

We develop an algorithm for bounding the rank of elliptic curves in the family $y^2=x^3-B x$, all of them with torsion group $\mathbb {Z} /(2 \mathbb {Z})$ and modular invariant $j=1728$. We use it to look for curves of high rank in this family and present four such curves of rank $13$ and $22$ of rank $12$.
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Bibliographic Information
  • Julián Aguirre
  • Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
  • Email: mtpagesj@lg.ehu.es
  • Fernando Castañeda
  • Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
  • Email: mtpcabrf@lg.ehu.es
  • Juan Carlos Peral
  • Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
  • MR Author ID: 137825
  • Email: mtppealj@lg.ehu.es
  • Received by editor(s): November 28, 2000
  • Received by editor(s) in revised form: July 5, 2002
  • Published electronically: May 30, 2003
  • Additional Notes: The second and third authors were supported by a grant from the University of the Basque Country.
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 73 (2004), 323-331
  • MSC (2000): Primary 11Y50
  • DOI: https://doi.org/10.1090/S0025-5718-03-01547-3
  • MathSciNet review: 2034125