Rank parity for congruent supersingular elliptic curves

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.

fixed a persistent typo in the results of Section 3. this typo led to the original example for p=3 being incorrect; it has been replaced with a correct example

References in corpus (1)

• Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields

Cited by in corpus (3)

• Root numbers and parity of local Iwasawa invariants
• Fine Selmer groups of congruent $p$-adic Galois representations
• Arithmetic properties of signed Selmer groups at non-ordinary primes