The Diophantine equationy2= x(x2+ 21Dx+ 112D2)and the conjectures of Birch and Swinnerton-Dyer

DOI10.1017/S1446788700020309zbMath0382.14006WikidataQ123114691 ScholiaQ123114691MaRDI QIDQ4161427

A. R. Rajwade

Publication date: 1977

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

elliptic curvecomplex multiplicationL-functionBSD conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Cubic and quartic Diophantine equations (11D25)

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Evaluation of Character Sums Connected with Elliptic Curves ⋮ Parametric families of elliptic curves with cyclic \(\mathbb F_p\)-rational points groups ⋮ Évaluation d'une somme cubique de caractères. (Evaluation of a cubic character sum) ⋮ Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums ⋮ Counting points on \(\text{CM}\) elliptic curves ⋮ Elliptic Curves and Primality Proving ⋮ On some determinants involving Jacobi symbols ⋮ Values of Gaussian hypergeometric series ⋮ CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS III ⋮ Evaluation of a cubic character sum using the \(\sqrt{-19}\) division points of the curve \(y^ 2=x^ 3-2^ 3\cdot 19x+2\cdot 19^ 2\)

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