Modular curves of the form X_0(N) are intrinsically interesting
curves to investigate. They contain a wealth of
information and cross over the boundaries of geometric,
algebraic, and analytic mathematics. We set out to compute
all of the information for a specific family of related modular
curves, namely X_0(N) for N|36. In this paper, we work out the
parameters for the curves, the coordinates of the important points
in relation to those parameters, and then we find equations for the
important maps between the curves. Also, since X_0(36) has genus
one, and therefore has a natural group structure, we include a
brief section on the subgroup generated by its cusps.