Sphere Packing Densities of Sublattices of the Mordell-Weil Lattices of two Families of Elliptic Curves

In this paper, we examine certain maximal rank sublattices of the Mordell-Weil lattices of two families of elliptic curves over fields of characteristic $p>0$. We compute explicit lower bounds on the densest sphere packings of these sublattices by finding lower bounds on the minimal norms of the sublattices and explicitly computing the volumes of their fundamental domains.