  The problem of classifying Einstein solvmanifolds, or equivalently, Ricci
soliton nilmanifolds, is known to be equivalent to a question on the variety of
n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine
which GL(n)-orbits in this variety have a critical point of the squared norm of
the moment map. In dimension 7, there are 148 complex nilpotent Lie algebras
and 6 curves of pairwise non-isomorphic nilpotent Lie algebras, and we give in
this paper a complete classification of the aforementioned distinguished
orbits.
