On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture

DOI10.1017/S0305004118000671OpenAlexW2890015376WikidataQ123191361 ScholiaQ123191361MaRDI QIDQ5207977

Shuai Zhai

Publication date: 14 January 2020

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

Full work available at URL: https://doi.org/10.1017/s0305004118000671

zbMATH Keywords

2-part of Birch--Swinnerton-Dyer conjecturecentral value of complex \(L\)-serieslower bound for 2-adic valuation

Mathematics Subject Classification ID

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

Uses Software

• ecdata

Cites Work

• Unnamed Item
• Non-vanishing theorems for quadratic twists of elliptic curves
• Congruent numbers and Heegner points
• A criterion for elliptic curves with second lowest 2-power in \(L(1)\). II
• A criterion for elliptic curves with lowest 2-power in L(1)
• The Conjecture of Birch and Swinnerton-Dyer
• On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication
• The Manin constant in the semistable case
• On the 2‐part of the Birch and Swinnerton‐Dyer conjecture for quadratic twists of elliptic curves
• A criterion for elliptic curves with lowest 2-power in L(1)
• A criterion for elliptic curves with lowest 2-power in L(1) (II) This work was supported by NSFC and RFDP.
• On thep-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of
• Computing the Degree of the Modular Parametrization of a Modular Elliptic Curve
• Congruent numbers with many prime factors
• Quadratic twists of elliptic curves
• PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES