Proceedings of the Japan Academy, Series A, Mathematical Sciences

On an elliptic curve over $\mathbf {Q}(t)$ of rank $\geq 9$ with a non-trivial 2-torsion point

Shoichi Kihara

Full-text: Open access

Abstract

We show an elliptic curve over $\mathbf{Q}(t)$ of rank at least 9 with a non-trivial 2-torsion point.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 1 (2001), 11-12.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393140

Digital Object Identifier
doi:10.3792/pjaa.77.11

Mathematical Reviews number (MathSciNet)
MR1812740

Zentralblatt MATH identifier
0989.11031

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

Keywords
Elliptic curve rank 2-torsion point

Citation

Kihara, Shoichi. On an elliptic curve over $\mathbf {Q}(t)$ of rank $\geq 9$ with a non-trivial 2-torsion point. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 1, 11--12. doi:10.3792/pjaa.77.11. https://projecteuclid.org/euclid.pja/1148393140


Export citation

References

  • Fermigier, S.: Exemples de courbes elliptiques de grand rang sur $\mathbf{Q}(t)$ et sur $\mathbf{Q}$ possédant des points d'order 2. C. R. Acad. Sci. Paris Sér. I Math., 322, 949–952 (1996).
  • Kihara, S.: Construction of high-rank elliptic curves with a non-trivial rational point of order 2. Proc. Japan Acad., 73A, 165 (1997).
  • Nagao, K.: Construction of high-rank elliptic curves with a non trivial torsion point. Math. Comp., 66, 411–415 (1997).