Ray class fields generated by torsion points of certain elliptic curves
Abstract
We first normalize the derivative Weierstrass '-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind η-function. And, by making use of this normalization of ' we associate certain elliptic curve to a given imaginary quadratic field K and then generate an infinite family of ray class fields over K by adjoining to K torsion points of such elliptic curve. We further construct some ray class invariants of imaginary quadratic fields by utilizing singular values of the normalization of ', as the y-coordinate in the Weierstrass equation of this elliptic curve, which would be a partial result for the Lang-Schertz conjecture of constructing ray class fields over K by means of the Siegel-Ramachandra invariant.