Ray class fields generated by torsion points of certain elliptic curves

Abstract

We first normalize the derivative Weierstrass a"similar to aEuro(2)-function appearing in the Weierstrass equations which give rise to analytic parametrizations of elliptic curves, by the Dedekind eta-function. And, by making use of this normalization of a"similar to aEuro(2), we associate a 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 an elliptic curve. We further construct some ray class invariants of imaginary quadratic fields by utilizing singular values of the normalization of a"similar to aEuro(2), as the y-coordinate in the Weierstrass equation of this elliptic curve, which would be a partial result towards the Lang-Schertz conjecture of constructing ray class fields over K by means of the Siegel-Ramachandra invariant.