Arenas, A.; Bayer, P. Complex multiplication points on modular curves. (English) Zbl 1102.11306 Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94, No. 3, 333-338 (2000). Summary: We generalize the concept of complex multiplication points on the modular curve \(X_0(N)\) to the case of any discriminant \(D\). We show how to reduce their study and evaluation of their number to that of primitive \(\mathcal O\)-ideals of type \(\alpha\mathcal O\) with the norm \(n(\alpha)\) equal to \(N\), where \(\mathcal O\) is the order of discriminant \(D\) of a quadratic field and, ultimately, to that of the primitive representations of \(N\) by the principal form of discriminant \(D\). When \(D<0\), explicit computations are exhibited. MSC: 11G15 Complex multiplication and moduli of abelian varieties 11G18 Arithmetic aspects of modular and Shimura varieties PDFBibTeX XMLCite \textit{A. Arenas} and \textit{P. Bayer}, Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94, No. 3, 333--338 (2000; Zbl 1102.11306) Full Text: EuDML