Rank parity for congruent supersingular elliptic curves

Hatley, Jeffrey

doi:10.1090/proc/13545

Rank parity for congruent supersingular elliptic curves
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Proc. Amer. Math. Soc. 145 (2017), 3775-3786 Request permission

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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