A recent paper of Shekhar compares the ranks of elliptic curves E 1 E_1 and E 2 E_2 for which there is an isomorphism E 1 [ p ] ≃ E 2 [ p ] E_1[p] \simeq E_2[p] as G a l ( Q ¯ / Q ) \mathrm {Gal}(\bar {\mathbf {Q}}/\mathbf {Q}) -modules, where p p is a prime of good ordinary reduction for both curves. In this paper we prove an analogous result in the case where p p is a prime of good supersingular reduction.