Frobenius distribution for pairs of elliptic curves

We will discuss a proof of the following result: let $E$ and $E’$ be two elliptic curves over a number field. Then there exist infinitely many primes $p$ such that the reductions mod $p$ of $E$ and $E’$ are geometrically isogenous. This result was previously known in the function field case, and can be seen as a partial analog of a density criterion for Hodge loci due to M. Green. It is related to the distribution of the traces of the Frobenius morphism.