Why $E/AutE$ is isomorphic to $\Bbb{P}^1$?

Question

Let $E$ be an elliptic curve which has complex multiplication over number field $K$.

Why $E/AutE$ is isomorphic to $\Bbb{P}^1$ ?

I tried to use first isomorphism theorem. Let $E→\Bbb{P}^1$ be $(x,y)→x$, but I cannot find it's kernel.