Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve

Tom Fisher

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arXiv · 2605.31488

Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve

Tom Fisher

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Abstract

We show that every pair of 2-torsion elements in the Tate-Shafarevich group of an elliptic curve are visible in the same abelian surface. This was previously only known for a single 2-torsion element. Our result explains some of the original observations on visibility in the paper of Cremona and Mazur.

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Tom Fisher. 2026-05-29. Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve. https://arxiv.org/abs/2605.31488

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