Variable in bound for #points in a elliptic curve over a finite field is a trace?

Question

I already know that the number of points $\#E(\mathbb{F}_q)$ in an elliptic curve over $\mathbb{F}_q$ is $q+1-t$, $|t| \le 2 \sqrt{q}$.

The thing is, the article 'Nonsingular Plane Cubic Curves over Finite Fields' by Schoof mentions that this $t$ is exactly the trace of the Frobenius endomorphism over $E$.

I couldn't find a reference for that claim. Does anybody have a proof or a link to it?