Analytic uniformization of CM elliptic curves.

Question

Let $E_{|F}$ be an elliptic curve defined over the number field $F$ with complex multiplication by an order $\mathcal{O}$ in its CM field $K$. It seems to be well known that one can choose an embedding of $F$ in $\mathbb{C}$ such that $E(\mathbb{C})\simeq \mathbb{C}/\mathcal{O}$. Can anyone explain how this is done? A priori $E(\mathbb{C})\simeq \mathbb{C}/\Lambda$ for some lattice $\Lambda\subseteq \mathbb{C}$. Can we choose an embedding so that such $\Lambda$ is homothetic to $\mathcal{O}$? Thanks.