I am teaching a graduate "classical" course on modular forms. I try to achieve the most elementary level for presenting modular polynomials. Serge Lang's "Elliptic functions" cover the topic quite well, except for some inconsistence (from my point of view) in using left/right cosets for actions of the modular group on the set of matrices of determinant $n$. I overcome this trouble by using one more simple arithmetic lemma which relates left and right cosets. I wonder whether there exist another version of the Kronecker--Weber approach for modular polynomials, or maybe even another *elementary* proof.



References for modular polynomials
I'm not quite sure what exactly you're asking for, but you might find the third part of David Cox's *Primes of the form x^2 + n y^2* useful for an elementary approach to modular polynomials.


