  Rank-2 Drinfeld modules are a function-field analogue of elliptic curves, and
the purpose of this paper is to investigate similarities and differences
between rank-2 Drinfeld modules and elliptic curves in terms of
supersingularity. Specifically, we provide an explicit formula of a
supersingular polynomial for rank-2 Drinfeld modules and prove several basic
properties. As an application, we give a numerical example of an asymptotically
optimal tower of Drinfeld modular curves.
