Is there an English reference for the analytic construction of the Hilbert class field of an imaginary quadratic field without using class field theory? I am in particular interested in a proof of the irreducibility of the class equation. For example Hasse seems to be doing that in Neue Begründung der komplexen Multiplikation. Zweiter Teil: Aufbau ohne Benutzung der allgemeinen Klassenkörpertheorie. but this is in German.

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    $\begingroup$ Perhaps II.4 (page 121) of Silverman's "Advanced topics in the arithmetic of Elliptic curves" is what you are looking for. Also, Iyanaga's "The theory of numbers" has an appendix on the history of class field theory, but I do not know if he mentions what you are asking. $\endgroup$ – EFinat-S Oct 27 '18 at 23:56

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