A criterion for elliptic curves with lowest 2-power in L(1)

DOI10.1017/S0305004196001247zbMath0882.11039MaRDI QIDQ4351086

Chunlai Zhao

Publication date: 1 October 1997

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

\(L\)-functionBirch-Swinnerton-Dyer conjecture2-descent2-divisibilitycongruent number problem

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (12)

Some exact formulae for the numbers of representations of integers by ternary quadratic forms ⋮ New series of odd non-congruent numbers ⋮ On several families of elliptic curves with arbitrary large Selmer groups ⋮ On elliptic curves \(y^{2} = x^{3}-n^{2}x\) with rank zero ⋮ Representation of integers by ternary quadratic forms. ⋮ On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture ⋮ 2-Selmer groups and the Birch-Swinnerton-Dyer conjecture for the congruent number curves ⋮ On the 2-adic valuations of central \(L\)-values of elliptic curves ⋮ On Quadratic Twists of Elliptic Curves and Some Applications of a Refined Version of Yu's Formula ⋮ A lower bound result for the central \(L\)-values of elliptic curves ⋮ A criterion for elliptic curves with second lowest 2-power in \(L(1)\). II ⋮ Congruent numbers

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