Modular Curves of Composite Level
Résumé
We examine a class of functions on $X_0 (N)$ where $N$ is the product of two arbitrary primes. The functions are built as products of Dedekind's $\eta$-function and play a role in the construction of elliptic curves with complex multiplication. We show how to determine the modular polynomials relating them to the absolute modular invariant $j$ and prove different properties of these polynomials. In particular, we show that they provide models for the modular curves $X_0 (N)$.