While reading Silverman's beautiful book The Arithmetic of Elliptic Curves, I was stuck trying to understand some elements of Example III.4.4:
First, I don't see why the case of characteristic 2 is excluded, what goes wrong in this case?
Second, what makes the ring homomorphism $\mathbf{Z}[i] \to End(E)$ sending $m+ni$ to $[m]+[n]\circ[i]$ an isomorphism in characteristic zero?
I'd really appreciate any hints.