Two invariants, two quartics and a sextic. They are connected by the relation 212 = 2 i f?0 - D3 -3 jf 3.
The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.
Three quintic forms f; (f, i) 1; (i 2, T)4 two sextic forms H; (H, 1)1 one septic form (i, T)2 one nonic form T.
For a further discussion of the binary sextic see Gordan, loc. cit., Clebsch, loc. cit.
The complete systems of the quintic and sextic were first obtained by Gordan in 1868 (Journ.