Rank Frequencies for Quadratic Twists of Elliptic Curves

DOI10.1080/10586458.2001.10504676zbMath1035.11025arXivmath/0010056OpenAlexW2020150618MaRDI QIDQ3146571

Karl Rubin, Alice Silverberg

Publication date: 12 September 2002

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010056

zbMATH Keywords

elliptic curvesMordell-Weil rankquadratic twists

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Global ground fields in algebraic geometry (14G25)

Related Items (19)

Rank jumps on elliptic surfaces and the Hilbert property ⋮ The rank of hyperelliptic Jacobians in families of quadratic twists ⋮ Vanishing of hyperelliptic \(L\)-functions at the central point ⋮ On the Vanishing of TwistedL-Functions of Elliptic Curves ⋮ Strong rational Diophantine \(D(q)\)-triples ⋮ On the typical rank of elliptic curves over \(\mathbb{Q}(T)\) ⋮ High rank elliptic curves with prescribed torsion group over quadratic fields ⋮ Rank gain of Jacobians over number field extensions with prescribed Galois groups ⋮ Low-lying zeros of families of elliptic curves ⋮ Injectivity of the specialization homomorphism of elliptic curves ⋮ High rank quadratic twists of pairs of elliptic curves ⋮ On a question of Frey and Jarden about the rank of Abelian varieties ⋮ On high rank \(\pi/3\) and \(2\pi/3\)-congruent number elliptic curves ⋮ Unnamed Item ⋮ On Quadratic Twists of Elliptic Curves and Some Applications of a Refined Version of Yu's Formula ⋮ The Sato-Tate conjecture and Nagao's conjecture ⋮ A heuristic for boundedness of ranks of elliptic curves ⋮ Ranks of elliptic curves ⋮ Class number problem for a family of real quadratic fields

Cites Work

• Rang de certaines familles de courbes elliptiques d'invariant donné
• The Square-Free Sieve and the Rank of Elliptic Curves

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