Computing polynomials of the Ramanujan {\(t_n\)} class invariants

Konstantinou, Elisavet and Kontogeorgis, Aristides

Abstract

We compute the minimal polynomials of the Ramanujan values tn , where n = 11 mod 24, using Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field ℚ(-n‾‾‾√), and have much smaller coeffcients than the Hilbert polynomials