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 -function. And, by making use of this normalization of we associate certain elliptic curve to a given imaginary quadratic field and then generate an infinite family of ray class fields over by adjoining to 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 -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 by means of the Siegel-Ramachandra invariant.
Cite
@article{arxiv.1007.2307,
title = {Ray class fields generated by torsion points of certain elliptic curves},
author = {Ja Kyung Koo and Dong Hwa Shin and Dong Sung Yoon},
journal= {arXiv preprint arXiv:1007.2307},
year = {2010}
}