Proceedings of the Japan Academy, Series A, Mathematical Sciences

On an elliptic curve over $\mathbf {Q}(t)$ of rank $\geq 14$

Shoichi Kihara

Full-text: Open access

Abstract

We show an elliptic curve over $\mathbf{Q}(t)$ of rank $\geq 14$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 4 (2001), 50-51.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393079

Digital Object Identifier
doi:10.3792/pjaa.77.50

Mathematical Reviews number (MathSciNet)
MR1829378

Zentralblatt MATH identifier
1015.11022

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

Keywords
Elliptic curve rank

Citation

Kihara, Shoichi. On an elliptic curve over $\mathbf {Q}(t)$ of rank $\geq 14$. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 4, 50--51. doi:10.3792/pjaa.77.50. https://projecteuclid.org/euclid.pja/1148393079


Export citation

References

  • Kihara, S.: On an infinite family of elliptic curves with rank $\geq 14$ over $\mathbf{Q}$. Proc. Japan Acad., 72A, 32 (1997).
  • Mestre, J.-F.: Courbes elliptiques de rang $\geq 11$ sur $\mathbf{Q}(t)$. C. R. Acad. Sci. Paris, 313, 139–142 (1991).
  • Mestre, J.-F.: Courbes elliptiques de rang $\geq 12$ sur $\mathbf{Q}(t)$. C. R. Acad. Sci. Paris, 313, 171–174 (1991).
  • Nagao, K.: An example of elliptic curve over $\mathbf{Q}(t)$ with rank $\geq 13$. Proc. Japan Acad., 70A, 152–153 (1994).