Lattice generated by doubly periodic periods

Let $\omega_1,\omega_2$ be complex numbers whose ratio is not real (i.e. they are the periods of a doubly periodic function). The set $\Omega(\omega_1,\omega_2)=\left\{ m \omega_1 +n\omega_2 \colon m,n \in \mathbb{Z} \right\}$ of integer linear combinations of $\omega_1$ and $\omega_2$ is called the lattice generated by $\omega_1$ and $\omega_2$.