I wonder why elliptic curve on complex field is a torus

Question

Let $ E(\mathbb{C})$ be an elliptic curve on $\mathbb{C}$.

$\Lambda $ be a lattices of periods.

I understood the proof of $\mathbb{C}/\Lambda \to E(\mathbb{C})$ is an isomorphism. But I think $\mathbb{C}/\Lambda$ is 2-dimmensional as vector space over $\mathbb{R}$, and $E(\mathbb{C})$ is 4-dimensional as vector space over $\mathbb{R}$. What am I missing?