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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 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights
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by Joseph H. Silverman PDF
Math. Comp. 68 (1999), 835-858 Request permission


Let $E/\mathbb {Q}$ be an elliptic curve of rank 1. We describe an algorithm which uses the value of $L’(E,1)$ and the theory of canonical heghts to efficiently search for points in $E(\mathbb {Q})$ and $E(\mathbb {Z}_{S})$. For rank 1 elliptic curves $E/\mathbb {Q}$ of moderately large conductor (say on the order of $10^{7}$ to $10^{10}$) and with a generator having moderately large canonical height (say between 13 and 50), our algorithm is the first practical general purpose method for determining if the set $E(\mathbb {Z}_{S})$ contains non-torsion points.
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Additional Information
  • Joseph H. Silverman
  • Affiliation: Mathematics Department, Box 1917, Brown University, Providence, RI 02912 USA
  • MR Author ID: 162205
  • ORCID: 0000-0003-3887-3248
  • Email:
  • Received by editor(s): May 8, 1996
  • Received by editor(s) in revised form: March 3, 1997
  • Additional Notes: Research partially supported by NSF DMS-9424642.
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 835-858
  • MSC (1991): Primary 11G05, 11Y50
  • DOI:
  • MathSciNet review: 1627825