an Example of Elliptic Curve over finite field has no CM

Question

I have known this property (from Silverman's The Arithmetic of Elliptic Curves): Let $\operatorname{char}(K)=p>0,$ and let $E/K$ be an elliptic curve with $j(E)~ \overline{\in}~ \overline{ \mathbb{F}}_{p}$, then $\operatorname{End}(E)=\mathbb{Z}$.

I want to see an example when $\operatorname{End}(E)=\mathbb{Z}$.

Thank you.

Answer 1

Elliptic curves with $j$-invariant lying in a finite field (or equivalently, in the algebraic closure of a finite field) always admit endomorphisms other than $\mathbb Z$.