Class invariants by Shimura's reciprocity law
Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 45-72.

On applique la loi de réciprocité de Shimura pour décider quand les valeurs des fonctions modulaires de haut niveau peuvent être utilisées pour engendrer le corps de classes de Hilbert d'un corps quadratique imaginaire. Lorsque c'est le cas, nous montrons aussi comment trouver le polynôme correspondant. Cela donne une preuve de certaines formules conjecturales de Morain et Zagier relatives à ces polynômes.

We apply the Shimura reciprocity law to determine when values of modular functions of higher level can be used to generate the Hilbert class field of an imaginary quadratic field. In addition, we show how to find the corresponding polynomial in these cases. This yields a proof for conjectural formulas of Morain and Zagier concerning such polynomials.

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Gee, Alice. Class invariants by Shimura's reciprocity law. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 45-72. http://www.numdam.org/item/JTNB_1999__11_1_45_0/

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