The Arithmetic of Elliptic Curves
《The Arithmetic of Elliptic Curves》 · 第 428 页 · Appendix C，Section 11「Complex Multiplication」，Theorem 11.5(b)
Let $K$ be an imaginary quadratic field, let $R\subset K$ be its ring of integers, and let $E/\mathbb C$ be an elliptic curve with $\operatorname{End}(E)\cong R$. The maximal abelian extension $K^{\mathrm{ab}}$ of $K$ is $K(j(E);\phi_E(T),T\in E_{\mathrm{tors}})$, the field obtained by adjoining to $K$ the $j$-invariant of $E$ and the value of a Weber function at all torsion points of $E$.