  Inspired by the work of S. Ramanujan, many people have studied generalized
modular equations and the numerous identities found by Ramanujan. These
identities known as modular equations can be transformed into polynomial
equations. There is no developed theory about how to find the degrees of these
polynomial modular equations explicitly. In this paper, we determine the
degrees of the polynomial modular equations explicitly and study the relation
between Hecke groups and modular equations in Ramanujan's theories of
signatures 2, 3, and 4.
