## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### On the rank of the elliptic curves with a rational point of order 4

Shoichi Kihara

#### Abstract

We construct an elliptic curve of rank at least 4 over $Q(t)$ with a rational point of order 4. We also show an infinite family of elliptic curves of rank at least 5 over $Q$ with a rational point of order4, which is parametrized by the rational points of an elliptic curve of rank at least 1.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 4 (2004), 26-27.

Dates
First available in Project Euclid: 18 May 2005

https://projecteuclid.org/euclid.pja/1116442212

Digital Object Identifier
doi:10.3792/pjaa.80.26

Mathematical Reviews number (MathSciNet)
MR2055072

Zentralblatt MATH identifier
1050.11058

Subjects

Keywords
Elliptic curve rank

#### Citation

Kihara, Shoichi. On the rank of the elliptic curves with a rational point of order 4. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 4, 26--27. doi:10.3792/pjaa.80.26. https://projecteuclid.org/euclid.pja/1116442212

#### References

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• Nagao, K.: On the rank of elliptic curve $y^2=x^3-kx$. Kobe J. Math., 11, 205–210 (1994).