Elliptic curves with no rational points

Nakagawa, Jin; Horie, Kuniaki

doi:10.1090/S0002-9939-1988-0958035-0

Elliptic curves with no rational points
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by Jin Nakagawa and Kuniaki Horie PDF

Proc. Amer. Math. Soc. 104 (1988), 20-24 Request permission

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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