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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?)

  • [1] A. Néron, "Problèmes arithmétiques et géométriques rattachés à la notion de rang d'une courbe algébrique dans un corps," Bull. Soc. Math. France, v. 80, 1952, pp. 101-166. MR 15, 151. MR 0056951 (15:151a)
  • [2] J. Tate, Rational Points on Elliptic Curves, Philips Lectures, Haverford College, 1961.
  • [3] A. Wiman, "Über rationale Punkte auf Kurven dritter Ordnung vom Geschlechte Eins," Acta Math., v. 80, 1948, pp. 223-257. MR 10, 472. MR 0028603 (10:472c)

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

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