On the rank of elliptic curves with three rational points of order 2. III

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On the rank of elliptic curves with three rational points of order 2. III

Shoichi Kihara

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 80, Number 3 (2004), 13-14.

Abstract

We construct an elliptic curve of rank at least 6 over $Q(t)$ with three non-trivial rational points of order 2.

First Page: Show

Primary Subjects: 11G05

Keywords: Elliptic curve; rank

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442133
Mathematical Reviews number (MathSciNet): MR2046259
Zentralblatt MATH identifier: 1050.11059
Digital Object Identifier: doi:10.3792/pjaa.80.13

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References

Dujella, A.: Diophantine triples and construction of high-rank elliptic curves over $Q$ with three non-trivial 2-torsion points. Rocky Mountain J. Math., 30, 157--164 (2000).

Mathematical Reviews (MathSciNet): MR1763803

Digital Object Identifier: doi:10.1216/rmjm/1022008982

Zentralblatt MATH: 0989.11032

Kihara, S.: On the rank of elliptic curves with three rational points of order 2. Proc. Japan Acad., 73A, 77--78 (1997).

Mathematical Reviews (MathSciNet): MR1470173

Kihara, S.: On the rank of elliptic curves with three rational points of order 2. II. Proc. Japan Acad., 73A, 151 (1997).

Mathematical Reviews (MathSciNet): MR1487582

Kulesz, L.: Courbes elliptiques de rang $\ge 5$ sur $Q(t)$ avec un groupe de torsion isomorphe á $Z/2Z\times Z/2Z$. C. R. Acad. Sci. Paris Sér. I Math., 329, 503--506 (1999).

Mathematical Reviews (MathSciNet): MR1715134

Digital Object Identifier: doi:10.1016/S0764-4442(00)80050-6

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