inverse elliptic nome

Solving the nome q for the parameter m gives m(q) | = | (ϑ_2^4(q))/(ϑ_3^4(q)) | = | (16η^8(1/2 τ) η^16(2τ))/(η^24(τ)), where ϑ_i(q) = ϑ_i(0, q) is a Jacobi theta function, η(τ) is the Dedekind eta function, and q = e^(i πτ) is the nome.

elliptic lambda function | Jacobi theta functions | nome