= Complex uniformization of an elliptic curve
{title2=$E(\mathbb C)\simeq\mathbb C/L$}
Every complex <elliptic curve>, as a complex Lie group, is the quotient of $\mathbb C$ by a rank-two lattice. The coordinate functions are built from the <Weierstrass elliptic function> and its derivative. Holomorphic group homomorphisms lift to scalar multiplication on $\mathbb C$, and their endomorphism condition is $aL\subseteq L$. This turns <complex multiplication> into a statement about lattice stabilizers.
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