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Ray class fields generated by torsion points of certain elliptic curves
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
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