On Quadratic Twists of Elliptic Curves and Some Applications of a Refined Version of Yu's Formula

DOI10.1080/00927872.2013.830731zbMath1296.11066arXiv1003.4393OpenAlexW3106509242MaRDI QIDQ5495297

Derong Qiu

Publication date: 31 July 2014

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4393

zbMATH Keywords

elliptic curveTate-Shafarevich groupquadratic twistcohomology groupHeegner point

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (1)

Arithmetic statistics and noncommutative Iwasawa theory

Cites Work

• Unnamed Item
• A classical Diophantine problem and modular forms of weight \(3/2\)
• Heegner points and derivatives of \(L\)-series
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• On the conjecture of Birch and Swinnerton-Dyer
• On Tate-Shafarevich groups over Galois extensions
• Rational points of Abelian varieties with values in towers of number fields
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Rank Frequencies for Quadratic Twists of Elliptic Curves
• Fudge Factors in the Birch and Swinnerton-Dyer Conjecture
• The Arithmetic of Elliptic Curves
• A criterion for elliptic curves with lowest 2-power in L(1)

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