The cardinality of the preimage of a point under a nonzero isogeny equals the separable degree of the isogeny

Question

Let $f:E_1\rightarrow E_2$ be a nonzero isogeny between elliptic curves.

Take a point $Q \in E_2$.

I am looking for a reference to a proof, or a proof, of the following fact:

$|f^{-1}(Q)|=\text{deg}_s(f)$

where $\text{deg}_s(f)$ is the separable degree of $f$.

In fact, it's enough to show that this is true for all but a finite set of points $Q$. The desired claim would then follow because $f$ is a group homomorphism.

EDIT:

1. I'm working over an algebraically closed field.
2. If you prefer to, you may assume that $f$ is a separable isogeny.