Each lattice L is given as
[gram, mass, rs, red_mass, hbv]
where:
-- gram is a Gram matrix of L
-- mass is the mass of L (inverse of order of isometry group of L)
-- rs is the root system of L (an ADE root system)
-- red_mass is the reduced mass of L (mass * order of the Weyl group of L)
-- hbv is the hashed BV invariant of L (see Unimodular Hunting II)