On the Birch-Swinnerton-Dyer conjecture of elliptic curves \(E_D:y^2 = x^3-D^2 x\)

DOI10.1007/s101140050017zbMath1080.11500OpenAlexW4255757384MaRDI QIDQ1578861

Ye Tian, Delang Li

Publication date: 30 July 2001

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s101140050017

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (10)

Congruent elliptic curves with non-trivial Shafarevich-Tate groups ⋮ Some new families of non-congruent numbers ⋮ Congruent numbers, quadratic forms and \(K_2\) ⋮ An extension theorem for generating new families of non-congruent numbers ⋮ Diophantine equations, class groups and non-congruent numbers ⋮ On the extension of even families of non-congruent numbers ⋮ The non-congruent numbers via Monsky’s formula ⋮ On non-congruent numbers with 1 modulo 4 prime factors ⋮ 2-Selmer groups and the Birch-Swinnerton-Dyer conjecture for the congruent number curves ⋮ A remark on prime (non)congruent numbers

Cites Work

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• A classical Diophantine problem and modular forms of weight \(3/2\)
• Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• A Relation Between the Two-Component of the Tate-Safarevic Group and L(1) for Certain Elliptic Curves
• Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture
• Notes on elliptic curves. II.

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