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arXiv · 1605.08382

Rank parity for congruent supersingular elliptic curves

Jeffrey Hatley
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Abstract

A recent paper of Shekhar compares the ranks of elliptic curves $E_1$ and $E_2$ for which there is an isomorphism $E_1[p] \simeq E_2[p]$ as $\mathrm{Gal}(\bar{\mathbf{Q}}/\mathbf{Q})$-modules, where $p$ is a prime of good ordinary reduction for both curves. In this paper we prove an analogous result in the case where $p$ is a prime of good supersingular reduction.

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Jeffrey Hatley. 2016-05-26. Rank parity for congruent supersingular elliptic curves. https://doi.org/10.1090/proc/13545

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