Greylag goose the western greylag goose, breeds in Iceland and north and central Europe; "A. a. rubrirostris", the eastern greylag goose, breeds in Romania, Turkey and Russia eastwards to northeastern China. The two subspecies intergrade where their ranges meet. The greylag goose sometimes hybridises with other species of goose including the barnacle goose ("Branta leucopsis") and the Canada goose ("Branta canadensis"), and occasionally with the mute swan ("Cygnus olor"). The greylag goose was one of the first animals to be domesticated; this happened at least 3000 years ago in Ancient Egypt, the domestic breed being known as "A. a. domesticus". As the
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":