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Mathematics of Computation

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A search for elliptic curves with large rank

Authors: David E. Penney and Carl Pomerance
Journal: Math. Comp. 28 (1974), 851-853
MSC: Primary 14G25; Secondary 10B10, 14G05
MathSciNet review: 0376686
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Abstract: A search procedure is described for finding elliptic curves with rational coefficients for which the group of rational points has large rank. Specific examples are given of elliptic curves with rank $\geqq 6$.

References [Enhancements On Off] (What's this?)

  • André Néron, Problèmes arithmétiques et géométriques rattachés à la notion de rang d’une courbe algébrique dans un corps, Bull. Soc. Math. France 80 (1952), 101–166 (French). MR 56951
  • J. Tate, Rational Points on Elliptic Curves, Philips Lectures, Haverford College, 1961.
  • A. Wiman, Über rationale Punkte auf Kurven dritter Ordnung vom Geschlechte Eins, Acta Math. 80 (1948), 223–257 (German). MR 28603, DOI

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Additional Information

Keywords: The rank of an elliptic curve
Article copyright: © Copyright 1974 American Mathematical Society