Construction of elliptic curves with large Iwasawa \(\lambda\)-invariants and large Tate-Shafarevich groups

DOI10.1007/s00229-006-0068-9zbMath1152.11045OpenAlexW1992115873MaRDI QIDQ946864

Kazuo Matsuno

Publication date: 25 September 2008

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-006-0068-9

zbMATH Keywords

Iwasawa invariantselliptic curveTate-Shafarevich groupGalois modules

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Iwasawa theory (11R23)

Related Items

Iwasawa invariants for elliptic curves over \(\mathbb{Z}_p\)-extensions and Kida's formula ⋮ On large Iwasawa \(\lambda\)-invariants of imaginary quadratic function fields ⋮ ON THE DISTRIBUTION OF IWASAWA INVARIANTS ASSOCIATED TO MULTIGRAPHS ⋮ \(\lambda\)-invariant stability in families of modular Galois representations ⋮ Potential \(\text Ш\) for abelian varieties ⋮ Arbitrarily large Tate-Shafarevich group on abelian surfaces ⋮ Large Shafarevich-Tate groups over quadratic number fields ⋮ Descent via isogeny on elliptic curves with large rational torsion subgroups ⋮ ON THE 2-ADIC IWASAWA INVARIANTS OF ORDINARY ELLIPTIC CURVES ⋮ Large Selmer groups over number fields ⋮ Arbitrarily large 2-torsion in Tate–Shafarevich groups of abelian varieties ⋮ Elliptic curves with exceptionally large analytic order of the Tate–Shafarevich groups

Uses Software

• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The \(p\)-part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large
• Elliptic curves with large Tate-Shafarevich groups over a number field
• On the Iwasawa invariants of elliptic curves
• Selmer groups of elliptic curves that can be arbitrarily large.
• Nonvanishing theorems for L-functions of modular forms and their derivatives
• ON THE 2-ADIC IWASAWA INVARIANTS OF ORDINARY ELLIPTIC CURVES
• On the Selmer Group of Twists of Elliptic Curves with Q-Rational Torsion Points
• FINITENESS OF $ E(\mathbf{Q})$ AND $ \textrm{Ø}(E,\mathbf{Q})$ FOR A SUBCLASS OF WEIL CURVES
• Elliptic Curves with no Rational Points
• Die Ordnung der Schafarewitsch‐Tate‐Gruppe kann beliebig groß werden
• On finite $\Lambda $-submodules of Selmer groups of elliptic curves
• Arithmetic on Curves of genus 1. VI. The Tate-Safarevic group can be arbitrarily large.
• Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer.
• Some examples of 5 and 7 descent for elliptic curves over \(\mathbb{Q}\)