Generation of class fields by using the Weber function

Abstract

Let K be an imaginary quadratic field and OK be its ring of integers. Let hE be the Weber function on a certain elliptic curve E with complex multiplication by OK. We show that if N (>1) is an integer prime to 6, then the function hE alone generates the ray class field modulo NOK over K when evaluated at some N-torsion point of E, which would be a partial answer to the question mentioned in [10, p. 105].