Elliptic curves and Thompson's sporadic simple group

Maryam Khaqan

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arXiv · 2008.01607

Elliptic curves and Thompson's sporadic simple group

Maryam Khaqan

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Abstract

We characterize all infinite-dimensional graded virtual modules for Thompson's sporadic simple group, whose graded traces are weight 3/2 weakly holomorphic modular forms satisfying certain special properties. We then use these modules to detect the non-triviality of Mordell--Weil, Selmer, and Tate--Shafarevich groups of quadratic twists of certain elliptic curves.

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Maryam Khaqan. 2020-08-04. Elliptic curves and Thompson's sporadic simple group. https://arxiv.org/abs/2008.01607

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