Computing Polynomials of the Ramanujan tn Class Invariants

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