  Let $E$ and $E'$ be 2-isogenous elliptic curves over $\Q$. Following
\cite{ck}, we call a good prime $p$ \emph{anomalous} if $E(\F_p) \simeq
E'(\F_p)$ but $E(\F_{p^2}) \not \simeq E'(\F_{p^2})$. Our main result is an
explicit formula for the proportion of anomalous primes for any such pair of
elliptic curves. We consider both the CM case and the non-CM case.
