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# Computing Polynomials of the Ramanujan $t_n$ Class Invariants

Published:2009-12-01
Printed: Dec 2009
• Elisavet Konstantinou
• Aristides Kontogeorgis
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## Abstract

We compute the minimal polynomials of the Ramanujan values $t_n$, where $n\equiv 11 \mod 24$, using the 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.
 MSC Classifications: 11R29 - Class numbers, class groups, discriminants 33E05 - Elliptic functions and integrals 11R20 - Other abelian and metabelian extensions

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