Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants

Abstract

We compute the minimal polynomials of the Ramanujan values $t_n$, where $n\equiv 11 \mod 24$, using Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field $\mathbb{Q}(\sqrt{-n})$, and have much smaller coefficients than the Hilbert polynomials.