On elliptic curves with large Tate-Shafarevich groups

DOI10.1006/JNTH.2000.2599zbMath1014.11039OpenAlexW2031469947MaRDI QIDQ5931321

Daisuke Atake

Publication date: 24 April 2001

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.2000.2599

zbMATH Keywords

Selmer groupsTate-Shafarevich group

Mathematics Subject Classification ID

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

Related Items (4)

ON SELMER GROUPS AND TATE–SHAFAREVICH GROUPS FOR ELLIPTIC CURVESy²=x³−n³ ⋮ ON SELMER GROUPS OF QUADRATIC TWISTS OF ELLIPTIC CURVES WITH A TWO‐TORSION OVER ⋮ Distribution of Selmer groups of quadratic twists of a family of elliptic curves ⋮ ON POSITIVE PROPORTION OF RANK-ZERO TWISTS OF ELLIPTIC CURVES OVER

Cites Work

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• On the equation \(Y^ 2=(X+p)(X^ 2+p^ 2)\)
• Computation of the Selmer groups of certain parametrized elliptic curves
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• A Family of Semistable Elliptic Curves with Large Tate-Shafarevitch Groups
• Die Ordnung der Schafarewitsch‐Tate‐Gruppe kann beliebig groß werden

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