From the results of Waterhouse, the explicit formula for the isomorphism classes of supersingular elliptic curves over any finite field is known.

In this talk, I will recall Honda-Tate theorem which help us parametrize the isogeny classes of simple abelian varieties over a finite field with elements. In each isogeny class, we provide a lattice description for superspecial abelian varieties over . Our description depends on the parity of the exponent of When is an odd power of the prime , we give an explicit formula for the number of superspecial abelian surfaces over

This is a joint work with Jiangwei Xue and Chia-Fu Yu