Silverman in his book Arithmetic of Elliptic Curves has given an example of an elliptic curve $E/K$ with complex multiplication: $$E: y^2=x^3-x$$
and the map $$[i]:E\longrightarrow E, \ \ \ (x,y)\rightarrow (-x,iy)$$
It is given that,
There is a ring homomorphism$$\mathbb{Z}[i]\longrightarrow \text{End}(E),\ \ \ m+ni\rightarrow [m]+[n]\circ[i]$$ If $\text{char}(K)=0$ then this map is an isomorphism, $\text{End}(E)\cong\mathbb{Z}[i].$
My question is,if $\text{char}(K)=0$ then why does it imply that $\text{End}(E)\cong\mathbb{Z}[i]$?
Note:I do not have any knowledge on the theory of Elliptic curves with CM other than the definition.