Proceedings of the Japan Academy, Series A, Mathematical Sciences

Nonexistence of elliptic curves having everywhere good reduction and cubic discriminant

Takaaki Kagawa

Full-text: Open access

Abstract

In this paper, it is proved that, over certain real quadratic fields, there are no elliptic curves having everywhere good reduction and cubic discriminant.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 9 (2000), 141-142.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393428

Digital Object Identifier
doi:10.3792/pjaa.76.141

Mathematical Reviews number (MathSciNet)
MR1801674

Zentralblatt MATH identifier
0991.11029

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52]

Keywords
Elliptic curves everywhere good reduction

Citation

Kagawa, Takaaki. Nonexistence of elliptic curves having everywhere good reduction and cubic discriminant. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 9, 141--142. doi:10.3792/pjaa.76.141. https://projecteuclid.org/euclid.pja/1148393428


Export citation

References

  • Fröhlich, A., and Taylor, M. J.: Algebraic number theory. Cambridge Stud. Adv. Math., 27, Cambridge Univ. Press, Cambridge (1991).
  • Kagawa, T.: Determination of elliptic curves with everywhere good reduction over real quadratic fields $\textbf{Q}(\sqrt{3p})$. Acta\hphantom. Arith. (to appear).
  • Lang, S.: Algebraic Number Theory. 2nd ed., Grad. Texts in Math., 110, Springer, Berlin-Heidelberg-New York (1994).