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manuscripta mathematica

, Volume 29, Issue 2–4, pp 183–194 | Cite as

On some elliptic curves defined over Q of free rank ≧9

  • Kumiko Nakata
Article
  • 31 Downloads

Abstract

Infinitely many elliptic curves defined over Q of free rank ≧9 are explicitly constructed.

Keywords

Number Theory Algebraic Geometry Elliptic Curve Topological Group Elliptic Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    GRUNEWALD, F.J., ZIMMERT, R.: Über einige rationale elliptische Kurven mit freien Rang ≧ 8. J. reine. angew. Math.,296, 100–107 (1977)Google Scholar
  2. [2]
    MORDELL, L.J.: Diophantine equations. London and New York, Academic Press, 1969Google Scholar
  3. [3]
    NÉRON, A.: Problèmes arithmétiques et géometriques rattachés à la notion de rang d'une courbe algebrique dans un corps. Bull. Soc. Math. France,80, 101–166 (1952)Google Scholar
  4. [4]
    NÉRON, A.: Propriétés arithmétiques de certaines familles de courbes algebriques. Proc. Int. Congress. Amsterdam,III, 481–488 (1954)Google Scholar
  5. [5]
    PENNY, D.E., POMERANCE, C.: Three elliptic curves with rank at least seven. Mathematics of Computation,29, 965–968 (1975)Google Scholar
  6. [6]
    PENNY, D.E., POMERANCE, C.: A search for elliptic curves with large rank. Mathematics of Computation,28, 851–853 (1974)Google Scholar
  7. [7]
    WIMAN, A.: Über den Rang von den Kurven y2=x(x+a) (x+b). Acta Math.,76, 225–251 (1944)Google Scholar
  8. [8]
    WIMAN, A.: Über rationale Punkte auf den Kurven y2=x(x2−c2). Acta Math.,77, 281–320 (1945)Google Scholar
  9. [9]
    WIMAN, A.: Über rationale Punkte auf Kurven dritter Ordnung vom Geschlechte eins. Acta Math.,80, 223–257 (1948)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Kumiko Nakata
    • 1
  1. 1.Department of MathematicsOsaka UniversityToyonaka, OsakaJapan

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