On the 2‐part of the Birch and Swinnerton‐Dyer conjecture for quadratic twists of elliptic curves

DOI10.1112/jlms.12284zbMath1455.11081arXiv1712.01271OpenAlexW2981545105WikidataQ122962422 ScholiaQ122962422MaRDI QIDQ3296753

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Publication date: 1 July 2020

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

Full work available at URL: https://arxiv.org/abs/1712.01271

zbMATH Keywords

elliptic curvesmodular symbolsBirch and Swinnerton-Dyer conjecture2-descentTamagawa factors

Mathematics Subject Classification ID

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

Related Items (3)

Quadratic twists of \(X_0(14)\) ⋮ On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture ⋮ Chromatic Selmer groups and arithmetic invariants of elliptic curves

Cites Work

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• Non-vanishing theorems for quadratic twists of elliptic curves
• Explicit Gross-Zagier and Waldspurger formulae
• Heegner points and derivatives of \(L\)-series
• The arithmetic of elliptic curves
• Prime twists of elliptic curves
• The Conjecture of Birch and Swinnerton-Dyer
• Selmer ranks of quadratic twists of elliptic curves with partial rational two-torsion
• The Manin constant in the semistable case
• FINITENESS OF $ E(\mathbf{Q})$ AND $ \textrm{Ø}(E,\mathbf{Q})$ FOR A SUBCLASS OF WEIL CURVES
• How to do a 𝑝-descent on an elliptic curve
• Heegner points on modular curves
• Quadratic twists of elliptic curves
• GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS
• PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES

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