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Let $K=\mathbb Q(\sqrt{-d})$ be any imaginary quadratic field. Let $O_{\mathcal{K}}$ be its maximal order and $O$ be any order. Let $m$ be the conductor of $K$. Is it possible to compute ring class field from ray class field?

Math123
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refer to my answer at the following https://math.stackexchange.com/a/803837/152394; which gives the idea of what an ring class field and ray class field is