This article is cited in 2 papers

The zeta-function of elliptic curves over certain Abelian extensions of imaginary quadratic fields

P. F. Kurchanov


Abstract: For certain elliptic curves defined over an imaginary quadratic field, the value at one of the canonical $L$-series of these curves with explicit Dirichlet characters of the ground field is proved to equal zero.
Bibliography: 9 titles.

UDC: 513.015.7

MSC: Primary 14G10, 14H25; Secondary 14K15, 10D20, 22E55, 20G05

Received: 15.03.1976

 English version: Mathematics of the USSR-Sbornik, 1977, 31:1, 49–62

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