  We study the general deformations of maximal eight-dimensional supergravity
by using the embedding tensor approach. The scalar potential induced by these
gaugings is determined. Subsequently, by combining duality covariance arguments
and algebraic geometry techniques, we find the complete set of critical points
of the scalar potential. Remarkably, up to SO(2) X SO(3) rotations there turns
out to be a unique theory admitting extrema. The gauge group of the theory is
CSO(2,0,1).
