From the pioneering work of Deuring one knows that there is an intimate relationship between elliptic curves in characteristic \(p\) and the arithmetic of the (definite-quaternion) division algebra \(H(p)\). Deuring's results were based on the class number formula of Eichler whose original proof was analytic. However, a geometric proof may be given by using the 1-1 correspondence between supersingular elliptic curves and left ideal classes in a maximal order in \(H(p)\). In this paper, the author carries out a similar program for function fields using supersingular Drinfeld modules. One obtains explicit expressions for certain class numbers as well as a ``mass'' formula.