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December 2006 A Remark on the Mordell-Weil Rank of Elliptic Curves over the Maximal Abelian Extension of the Rational Number Field
Emi KOBAYASHI
Tokyo J. Math. 29(2): 295-300 (December 2006). DOI: 10.3836/tjm/1170348168

Abstract

In this paper, we study the Mordell-Weil ranks of elliptic curves defined over the maximal abelian extension of the rational number field, assuming several conjectures on the Hasse-Weil $L$-functions. We prove that an elliptic curve defined over an abelian field with odd degree has infinite rank over the maximal abelian extension of the rational number field. This result gives affirmative evidence for 'the largeness' (in the sense of Pop) of the maximal abelian extension of the rational number field.

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Emi KOBAYASHI. "A Remark on the Mordell-Weil Rank of Elliptic Curves over the Maximal Abelian Extension of the Rational Number Field." Tokyo J. Math. 29 (2) 295 - 300, December 2006. https://doi.org/10.3836/tjm/1170348168

Information

Published: December 2006
First available in Project Euclid: 1 February 2007

zbMATH: 1213.11119
MathSciNet: MR2284973
Digital Object Identifier: 10.3836/tjm/1170348168

Rights: Copyright © 2006 Publication Committee for the Tokyo Journal of Mathematics

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Vol.29 • No. 2 • December 2006
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