On the rank of the elliptic curve $y^2 = x^3 + kx$. II
Shoichi Kihara
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 80, Number 4
(2004), 24-25.
Abstract
We construct an elliptic curve of the form $y^2 = x^3 + kx$ with rank at least 6 over $Q(x_1, x_2, x_3)$.
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11G05
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442211
Mathematical Reviews number (MathSciNet): MR2055071
Zentralblatt MATH identifier: 1050.11057
Digital Object Identifier: doi:10.3792/pjaa.80.24
References
Kihara, S.: On the rank of the elliptic curve $y^2=x^3+kx$. Proc. Japan Acad., 74A, 115--116 (1998).
Mathematical Reviews (MathSciNet): MR1658862
Mestre, J.-F.: Rang de courbes elliptiques d'invariant donné. C. R. Acad. Sci. Paris Sér. I Math., 314, 919--922 (1992).
Mathematical Reviews (MathSciNet): MR1168325
Nagao, K.: On the rank of elliptic curve $y^2=x^3-kx$. Kobe J. Math., 11, 205--210 (1994).
Mathematical Reviews (MathSciNet): MR1329432
Proceedings of the Japan Academy, Series A, Mathematical Sciences
