Modular curves of the form X0(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 X0(N) for those integers N dividing 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 X0(36) has genus one, and therefore has a natural group structure, we include a brief section
on the subgroup generated by its cusps.