Open Access
Sept. 2001 A note on the Selmer group of the elliptic curve $y^2 = x^3 + Dx$
Takeshi Goto
Proc. Japan Acad. Ser. A Math. Sci. 77(7): 122-125 (Sept. 2001). DOI: 10.3792/pjaa.77.122

Abstract

We present an explicit formula for the Selmer rank of the elliptic curve $y^2 = x^3 + Dx$. Using this formula, we give some results analogous to Iskra's theorem.

Citation

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Takeshi Goto. "A note on the Selmer group of the elliptic curve $y^2 = x^3 + Dx$." Proc. Japan Acad. Ser. A Math. Sci. 77 (7) 122 - 125, Sept. 2001. https://doi.org/10.3792/pjaa.77.122

Information

Published: Sept. 2001
First available in Project Euclid: 23 May 2006

MathSciNet: MR1857288
zbMATH: 1040.11042
Digital Object Identifier: 10.3792/pjaa.77.122

Subjects:
Primary: 11G05
Secondary: 14H52

Keywords: congruent number , Elliptic curve , Selmer group

Rights: Copyright © 2001 The Japan Academy

Vol.77 • No. 7 • Sept. 2001
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