Cackling goose Cackling goose The cackling goose ("Branta hutchinsii") is a North American bird of the genus "Branta" of black geese, which contains species with largely black plumage, distinguishing them from the grey "Anser" species. The black head and neck with white "chinstrap" distinguish this goose from all other geese except the larger Canada goose ("Branta canadensis") and the similarly sized barnacle goose ("B. leucopsis"). There are up to 5 subspecies of cackling goose, of varying sizes and plumage details. The female looks virtually identical but is slightly lighter and has a different voice. Some are hard to distinguish from the Canada
Genus of a quadratic form the same genus have equal discriminant and hence there are only finitely many equivalence classes in a genus. The Smith–Minkowski–Siegel mass formula gives the "weight" or "mass" of the quadratic forms in a genus, the count of equivalence classes weighted by the reciprocals of the orders of their automorphism groups. For binary quadratic forms there is a group structure on the set "C" equivalence classes of forms with given discriminant. The genera are defined by the "generic characters". The principal genus, the genus containing the principal form, is precisely the subgroup "C" and the genera are the cosets of "C":