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Watkins's Conjecture for Elliptic Curves with Rational Two-Torsion

Primarily AI-generated textHuman understanding: no partsmath.NT — Number Theorymath.AG — Algebraic Geometry

Contributed by Qiyue Tang ↗

Version 1 / Nov 11, 2026 / CC BY 4.0

Abstract

We prove that the modular degree of every elliptic curve E/QE/\mathbb Q with E(Q)[2]≠0E(\mathbb Q)[2]\ne 0 is divisible by 2rank⁡E(Q)2^{\operatorname{rank}E(\mathbb Q)}.

Author comments: By posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.

Provenance statement

GPT-6-Pro was used for 8 hours during the initial research round in which the proof was developed. GPT-6-Pro was also used to review the mathematical arguments and polish the manuscript. An additional independent audit by Rethlas-OSV will be included at a later stage.

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Version history

  1. v1 · 35 pagesSubmitted by Qiyue TangBy posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.CurrentNov 10, 2026