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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Construction of high-rank elliptic curves with a nontrivial torsion point
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by Koh-ichi Nagao PDF
Math. Comp. 66 (1997), 411-415 Request permission


We construct a family of infinitely many elliptic curves over $\mathbb {Q}$ with a nontrivial rational 2-torsion point and with rank $\ge$ 6, which is parametrized by the rational points of an elliptic curve of rank $\ge$ 1.
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Additional Information
  • Koh-ichi Nagao
  • Affiliation: Shiga Polytecnic College, 1414 Furukawa Cho, Oh-Mihachiman Shiga 523, Japan
  • Email:
  • Received by editor(s): June 16, 1994
  • Received by editor(s) in revised form: November 1, 1994, and November 13, 1995
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 411-415
  • MSC (1991): Primary 11G05, 11D25; Secondary 11Y50
  • DOI:
  • MathSciNet review: 1370855