Let $E_1$ and $E_2$ be elliptic curves defined over a number field $K$. Suppose that for all but finitely many primes $\ell$, and for all finite extension fields $L/K$,

$${\dim }_{{\mathbb{F}}_{\ell }}{\mathrm{Sel}}_{\ell }(L,E_1)={\dim }_{{\mathbb{F}}_{\ell }}{\mathrm{Sel}}_{\ell }(L,E_2).$$ We prove that $E_1$ and $E_2$ are isogenous over $K$.