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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Elliptic curves with no rational points


Authors: Jin Nakagawa and Kuniaki Horie
Journal: Proc. Amer. Math. Soc. 104 (1988), 20-24
MSC: Primary 11R45; Secondary 11D25, 11G05, 11R11, 14G25
DOI: https://doi.org/10.1090/S0002-9939-1988-0958035-0
MathSciNet review: 958035
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Abstract: The existence of infinitely many elliptic curves with no rational points except the origin $ \infty $ is proved by refining a theorem of Davenport-Heilbronn. The existence of infinitely many quadratic fields with the Iwasawa invariant $ {\lambda _3} = 0$ is proved at the same time.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0958035-0
Keywords: Elliptic curve, rational point, Iwasawa invariant, class number
Article copyright: © Copyright 1988 American Mathematical Society