Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture

DOI10.4064/aa-75-1-71-83zbMath0838.11039OpenAlexW965349518WikidataQ114022065 ScholiaQ114022065MaRDI QIDQ4855038

Ke Qin Feng

Publication date: 9 January 1996

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/206863

zbMATH Keywords

elliptic curverational pointBirch-Swinnerton-Dyer conjecturenon-congruent numbers

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Cubic and quartic Diophantine equations (11D25)

Related Items (15)

Some new families of non-congruent numbers ⋮ Congruent numbers, quadratic forms and \(K_2\) ⋮ Families of non-congruent numbers with odd prime factors of the form \(8k + 3\) ⋮ New series of odd non-congruent numbers ⋮ An extension theorem for generating new families of non-congruent numbers ⋮ On the extension of even families of non-congruent numbers ⋮ Families of even non-congruent numbers with prime factors in each odd congruence class modulo eight ⋮ The non-congruent numbers via Monsky’s formula ⋮ Joint distribution for the Selmer ranks of the congruent number curves ⋮ Distribution of Selmer groups of quadratic twists of a family of elliptic curves ⋮ Infinitely many hyperelliptic curves with exactly two rational points ⋮ Families of non-congruent numbers with arbitrarily many prime factors ⋮ Congruent Number Theta Coefficients to 1012 ⋮ 2-Selmer groups and the Birch-Swinnerton-Dyer conjecture for the congruent number curves ⋮ On the Birch-Swinnerton-Dyer conjecture of elliptic curves \(E_D:y^2 = x^3-D^2 x\)

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