Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 004-02. A pointwise 2-converse for elliptic curves with rational two-torsion
Manuscript map · lines 2525–2534
OpenAI@2026-10-07#rem:oai-p-004-02
Authors: OpenAI. Family 004.
Title: A pointwise 2-converse for elliptic curves with rational two-torsion.
Abstract: We prove a pointwise 2-converse for elliptic curves over ${}mathbf Q$ with nonzero rational two-torsion: if the $2{}{}infty$-Selmer corank is zero or one, then the analytic rank and Mordell–Weil rank equal that corank, and the Shafarevich–Tate group is finite. The result allows arbitrary reduction at 2.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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