 Complex lattice

A complex lattice is a discrete rank-two subgroup of the complex plane, generated by two real-linearly independent periods. An oriented basis can be chosen with $\mathrm{Im}({\omega }_1/{\omega }_2)>0$. Scaling by ${\omega }_2^{-1}$ then gives $\mathbb{Z}\tau +\mathbb{Z}$ for a point in the complex upper half-plane.