Let $E_1$ and $E_2$ be elliptic curves defined over a number field $K$ and without complex multiplication. We denote by ${\cal{F}}_{E_1, E_2}$ the set of non-zero prime ideals of $K$ for which the Frobenius fields of $E_1$ and $E_2$ coincide. It is known that the elliptic curves $E_1$ and $E_2$ are potentially isogenous if and only if ${\cal{F}}_{E_1, E_2}$ has a positive upper density within the set of primes of $K$. In light of this result, we discuss the growth of the function that counts the primes in ${\cal{F}}_{E_1, E_2}$ of norm at most $x$, for a positive real number $x$. This is joint work with Auden Hinz and Tian Wang.