Rational orbits of the space of pairs of exceptional Jordan algebras

Let k be a field of characteristic not equal to 2,3, O an octonion over k and J the exceptional Jordan algebra defined by O. We consider the prehomogeneous vector space (G,V) where G=GE6×GL(2) and V=J⊕J. We prove that generic rational orbits of this prehomogeneous vector space are in bijective correspondence with k-isomorphism classes of pairs (M,n) where M's are isotopes of J and n's are cubic étale subalgebras of M. Also we prove that if O is split, then generic rational orbits are in bijective correspondence with isomorphism classes of separable extensions of k of degrees up to 3.