  In their well known book Tsfasman and Vladut introduced a construction of a
family of function field lattices from algebraic curves over finite fields,
which have asymptotically good packing density in high dimensions. In this
paper we study geometric properties of lattices from this construction applied
to elliptic curves. In particular, we determine the generating sets, conditions
for well-roundedness and a formula for the number of minimal vectors. We also
prove a bound on the covering radii of these lattices, which improves on the
standard inequalities.
