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, Volume 95, Issue 1, pp 1–10 | Cite as

On certain twisted families of elliptic curves of rank 8

  • Hizuru Yamagishi


Elliptic Curve Rational Point Elliptic Curf Hyperelliptic Involution Rational Function Field 
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  1. [1]
    J. W. S. Cassels,Lectures on elliptic curves, London Mathematical Society student texts 24, Cambridge university press, 1991.Google Scholar
  2. [2]
    J. S. Chahal,Topics in number theory, Plenum press, 1988.Google Scholar
  3. [3]
    S. Fermigier, Construction of high-rank elliptic curves overQ andQ(t) with non-trivial 2-torsion,Proc. ANTS-II, Bordeaux 1996, LN Comp. Sci., Springer-Verlag, 1996, pp. 115–120.Google Scholar
  4. [4]
    F. Hazama, The Mordell-Weil group of certain abelian varieties defined over the rational function field,Tohoku Math. J. 44 (1992), 335–344.zbMATHGoogle Scholar
  5. [5]
    F. Hazama, Rational points on certain abelian varieties over function fields,J. Number Theory 50 (1995), 278–285.zbMATHCrossRefGoogle Scholar
  6. [6]
    J.-F. Mestre, Courbes elliptiques de rang ≥ 12 surQ(t),C. R. Acad. Sci. Paris, Sér. I,313 (1991), 171–174.zbMATHGoogle Scholar
  7. [7]
    H. Yamagishi, On the existence of elliptic curves of Mordell-Weil rank 6 with 4 parameters,Journal of Algebra 181 (1996), 558–564.zbMATHCrossRefGoogle Scholar
  8. [8]
    H. Yamagishi, A unified method of construction of elliptic curves with high Mordell-Weil rank, Doctoral thesis, Tokyo Denki University, 1996.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Hizuru Yamagishi
    • 1
  1. 1.College of Science and Engineering Department of Information SciencesTokyo Denki UniversitySaitamaJapan

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