Endomorphism of an elliptic curve (reviewed)

An endomorphism of an elliptic curve defined over a field $K$ is a homomorphism $\varphi\colon E\to E$ defined over $K$. The set of all endomorphisms of $E$ forms a ring called the endomorphism ring of $E$, denoted $\End(E)$, a special case of the endomorphism ring of an abelian variety.