  We consider even unimodular lattices which are critical for potential energy
with respect to Gaussian potential functions in the manifold of lattices having
point density 1. All even unimodular lattices up to dimension 24 are critical.
We show how to determine the Morse index in these cases. While all these
lattices are either local minima or saddle points, we find lattices in
dimension 32 which are local maxima. Also starting from dimension 32 there are
non-critical even unimodular lattices.
