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.

Author Bio

In the summer before his senior year at the University of Rochester, Tim began work on the research project that gave way to his paper. He worked with a professor he had recently been a Teaching Assistant for, Dr. Ken McMurdy, on applying some of the results from his doctoral work to a specific family of modular curves. When not doing mathematics, Tim can be found singing in an on campus a cappella choir called After Hours which he helped found.