Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields

Summary: We present algorithms for computing j -invariants, modular polynomials and explicit isogenies for ordinary rank 2 Drinfeld modules over finite fields and describe how Drinfeld modular polynomials can be used to compute isogeny graphs and endomorphism rings of ordinary rank 2 Drinfeld modules. Our technique for computing Drinfeld modular polynomials is based on the traditional analytic approach for obtaining classical modular polynomials. Our ideas for generating isogeny graphs and finding endomorphism rings for rank 2 Drinfeld modules closely follows the work of Kohel and Fouquet. All our algorithms were implemented in SAGE and numerical examples are included. For the entire collection see [Zbl 1461.11002].