Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the rank of elliptic curves with a reational point of order 3

Shoichi Kihara

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Abstract

We construct an elliptic curve over $\mathbf{Q}(t)$ of rank at least 6 with a rational point of order 3.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 8 (2000), 126-127.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393456

Digital Object Identifier
doi:10.3792/pjaa.76.126

Mathematical Reviews number (MathSciNet)
MR1794569

Zentralblatt MATH identifier
0959.11024

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

Keywords
Elliptic curve rank point of order 3

Citation

Kihara, Shoichi. On the rank of elliptic curves with a reational point of order 3. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 8, 126--127. doi:10.3792/pjaa.76.126. https://projecteuclid.org/euclid.pja/1148393456


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References

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  • Top, J.: Descent by 3-isogeny and 3-rank of quadratic fields. Advances in Number Theory. Oxford Science Publications, Oxford Univ. Press, Oxford, pp. 303–317 (1993).