We study a mass of the group of self-quasi-isogenies of the abelian variety corresponding to a point on the basic locus in the reduction modulo p of a GU(r, s) Shimura variety. We give explicit formulas for the number of irreducible components of the basic locus, and for the cardinality of the zero-dimensional Ekedahl-Oort stratum, in a Shimura variety associated with a unimodular Hermitian lattice. On the way, we also give a formula for the number of connected components of a Shimura variety. This is joint work with Chia-Fu Yu.