On the Drinfeld modular polynomial \(\Phi_ T(X,Y)\)
In a fashion similar to classical elliptic modular theory, one may attach to every monic, nonconstant \(f\in \mathbb{F}_q [T]\) a modular polynomial in the theory of Drinfeld modules. This polynomial gives much information, such as a model for the function field of the modular curve \(X_0 (f)\), etc. In this paper, the modular polynomial associated to \(f=T\) is studied. An algorithm for its computation is given and applications to supersingular invariants, Brandt matrices, and elliptic curves are presented.
scientific article; zbMATH DE number 765161