This is calculated by means of the inverse image of an appropriate random subvariety of the target.
i1 : Phi = last graph rationalMap PP_(ZZ/300007)^(1,4);
o1 : MultirationalMap (rational map from 4-dimensional subvariety of PP^4 x PP^5 to PP^5)
i2 : for i in {4,3,2,1,0} list time multidegree(i,Phi)
-- used 0.00106579 seconds
-- used 0.0974411 seconds
-- used 0.135768 seconds
-- used 0.11775 seconds
-- used 0.0884407 seconds
o2 = {51, 28, 14, 6, 2}
o2 : List
i3 : time assert(oo == multidegree Phi)
-- used 0.103784 seconds