Defining equations of modular curves
Journal
Advances in Mathematics
Journal Volume
204
Journal Issue
2
Pages
481-508
Date Issued
2006
Author(s)
Abstract
We obtain defining equations of modular curves X0 (N), X1 (N), and X (N) by explicitly constructing modular functions using generalized Dedekind eta functions. As applications, we describe a method of obtaining a basis for the space of cusp forms of weight 2 on a congruence subgroup. We also use our model of X0 (37) to find explicit modular parameterization of rational elliptic curves of conductor 37. © 2005 Elsevier Inc. All rights reserved.
Type
journal article