5-torsion in the Shafarevich-Tate group of a family of elliptic curves

DOI10.1006/jnth.1999.2493zbMath0983.11029OpenAlexW2049677520MaRDI QIDQ1587655

Cheryl DeLorme Beaver

Publication date: 10 April 2002

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

Full work available at URL: https://doi.org/10.1006/jnth.1999.2493

zbMATH Keywords

elliptic curveShafarevich-Tate groupSelmer groupCassels-Tate pairing5-torsion

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Global ground fields in algebraic geometry (14G25)

Related Items

Elements of class groups and Shafarevich-Tate groups of elliptic curves, Explicit isogeny descent on elliptic curves, Descent via isogeny on elliptic curves with large rational torsion subgroups, The Cassels-Tate pairing and the Platonic solids.

Cites Work

• Heegner points and derivatives of \(L\)-series
• Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
• On the Shafarevich-Tate group of the Jacobian of a quotient of the Fermat curve
• Some remarks concerning points of finite order on elliptic curves over global fields
• Modular elliptic curves and Fermat's Last Theorem
• Modèles minimaux des variétés abéliennes sur les corps locaux et globaux
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights
• Arithmetic on Curves of genus 1. VI. The Tate-Safarevic group can be arbitrarily large.
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