Nagoya Mathematical Journal

A Mordell-Weil group of rank $8$, and a subgroup of finite index

Charles F. Schwartz

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Article information

Nagoya Math. J., Volume 93 (1984), 19-26.

First available in Project Euclid: 14 June 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J27: Elliptic surfaces
Secondary: 11D41: Higher degree equations; Fermat's equation 14G05: Rational points 14K10: Algebraic moduli, classification [See also 11G15]


Schwartz, Charles F. A Mordell-Weil group of rank $8$, and a subgroup of finite index. Nagoya Math. J. 93 (1984), 19--26.

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  • [1] Cox, D. A. and Zucker, S., Intersection numbers of sections of elliptic surfaces, Invent. Math., 53 (1979), 1-44.
  • [2] Schwartz, C. F., On a family of elliptic surfaces with Mordell-Weil rank 4, to appear.
  • [3] Shioda, T., On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 20-59.
  • [4] Schwartz, C. F., An elliptic surface of Mordell-Weil rank 8 over the rational numbers, to appear. Department of Mathematics Rider College P.O. Box 64-00, Lawrencevlle New Jersey 08640 USA