Duke Mathematical Journal

Mordell-Weil groups of elliptic curves over C(t) with pg=0 or 1

David A. Cox

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J., Volume 49, Number 3 (1982), 677-689.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14K07
Secondary: 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35} 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]


Cox, David A. Mordell-Weil groups of elliptic curves over $\mathbf{C}(t)$ with $p_g=0$ or $1$. Duke Math. J. 49 (1982), no. 3, 677--689. doi:10.1215/S0012-7094-82-04935-3. https://projecteuclid.org/euclid.dmj/1077315384

Export citation


  • [1] D. A. Cox and W. R. Parry, Torsion in elliptic curves over $k(t)$, Compositio Math. 41 (1980), no. 3, 337–354.
  • [2] D. A. Cox and S. Zucker, Intersection numbers of sections of elliptic surfaces, Invent. Math. 53 (1979), no. 1, 1–44.
  • [3] E. Horikawa, Surjectivity of the period map of $\rm K3$ surfaces of degree $2$, Math. Ann. 228 (1977), no. 2, 113–146.
  • [4a] K. Kodaira, On compact analytic surfaces. II, Ann. of Math. (2) 77 (1963), 563–626.
  • [4b] K. Kodaira, On compact analytic surfaces. III, Ann. of Math. (2) 78 (1963), 1–40.
  • [5] J. Milnor and D. Husemoller, Symmetric bilinear forms, Springer-Verlag, New York, 1973.
  • [6] I. I. Pjateckiĭ-Šapiro and I. R. Šafarevič, Torelli's theorem for algebraic surfaces of type $\rm K3$, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 530–572.
  • [7] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan 24 (1972), 20–59.