Disparity in Selmer ranks of quadratic twists of elliptic curves

DOI10.4007/annals.2013.178.1.5zbMath1300.11063arXiv1111.2321OpenAlexW3099755295WikidataQ116215909 ScholiaQ116215909MaRDI QIDQ355138

Karl Rubin, Zev Klagsbrun, Barry Mazur

Publication date: 24 July 2013

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.2321

zbMATH Keywords

elliptic curvesSelmer groupsquadratic twistsparity

Mathematics Subject Classification ID

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

Related Items (25)

Compatibility of arithmetic and algebraic local constants (the case ) ⋮ The ℓ-parity conjecture over the constant quadratic extension ⋮ Non-isotrivial elliptic surfaces with non-zero average root number ⋮ Disparity in Selmer ranks of quadratic twists of elliptic curves ⋮ Quadratic twists of abelian varieties and disparity in Selmer ranks ⋮ Erratum to: ``Disparity in Selmer ranks of quadratic twists of elliptic curves ⋮ The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k ⋮ Selmer ranks of twists of hyperelliptic curves and superelliptic curves ⋮ 2‐Selmer parity for hyperelliptic curves in quadratic extensions ⋮ Selmer ranks of quadratic twists of elliptic curves with partial rational two-torsion ⋮ Strong Selmer companion elliptic curves ⋮ Root numbers and parity phenomena ⋮ The work of Barry Mazur ⋮ Large Shafarevich-Tate groups over quadratic number fields ⋮ 2-Selmer groups, 2-class groups and rational points on elliptic curves ⋮ The number of twists with large torsion of an elliptic curve ⋮ The even parity Goldfeld conjecture: congruent number elliptic curves ⋮ \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field ⋮ $2$-Selmer near-companion curves ⋮ On conjectural rank parities of quartic and sextic twists of elliptic curves ⋮ Selmer companion curves ⋮ Big fields that are not large ⋮ How many rational points does a random curve have? ⋮ A Markov model for Selmer ranks in families of twists ⋮ ON SELMER RANK PARITY OF TWISTS

Uses Software

• ecdata

Cites Work

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• Disparity in Selmer ranks of quadratic twists of elliptic curves
• On the ranks of the 2-Selmer groups of twists of a given elliptic curve
• Regulator constants and the parity conjecture
• Ranks of twists of elliptic curves and Hilbert's tenth problem
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
• Galois Cohomology
• Generalizing the Birch-Stephens theorem. I: Modular curves
• Twisting commutative algebraic groups
• Finding large Selmer rank via an arithmetic theory of local constants
• Galois properties of points of finite order of elliptic curves
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Random maximal isotropic subspaces and Selmer groups
• The effect of twisting on the 2-Selmer group
• Elliptic curves with all quadratic twists of positive rank
• Arithmetic of Elliptic Curves Upon Quadratic Extension
• The Heegner point Kolyvagin system
• Euler Systems
• Explicit n-descent on elliptic curves, I. Algebra
• Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer.

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