\] The point $P_{q,b}$ is defined over the narrow ring class field extension $K_{\mathcal{O}}^+$ of $K$ associated to the order ${\mathcal{O}}$. If $\alpha \in {{\rm Pic}}({\mathcal{O}})^+$, then ${{\rm rec}}(\alpha)(P_{q,b}) = \alpha * P_{q,b}$, where ${{\rm rec}}: {{\rm Pic}}^+ {\mathcal{O}}{\rightarrow}{\rm Gal}(K_{\mathcal{O}}^+/K)$ is the reciprocity isomorphism of class field theory