Generalised Weber Functions

A generalised Weber function is given by wN(z) = η(z/N)/η(z), where η(z) is the Dedekind function and N is any integer; the original function corresponds to N = 2. We classify the cases where some power w e evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating wN(z) and j(z).