Nome

Summary

The nome is the variable $q = e^{\pi i\tau}$ in which theta functions and elliptic functions are expanded as power series. For a real modulus $0 < k < 1$ it is $q = \exp(-\pi K'/K)$, where $K$ and $K'$ are complete elliptic integrals of the first kind. It ties the modulus of the Jacobi elliptic functions to the period ratio of their lattice.