In this talk a lattice will mean a discrete subgroup Λ of n-dimensional Euclidean space; the sphere packing associated to Λ is the arrangement of congruent spheres of radius equal to one half the minimum distance of Λ and centered at the lattice points.  The main parameter under consideration will be the packing density of the arrangement of spheres.  With this in mind, a family of p-dimensional lattices will be constructed from submodules M of the ring of integers of a cyclic number filed L of degree p, where p is an odd unramified prime in L/Q.  The density of the associated sphere packing will be determined in terms of the nonzero minimum of the trace form in M and the discriminant of L.