Assuming JC(2)is false,we define B to be the minimum of the gcd of the degrees of P and Q,where(P,Q)runs over the counterexamples of JC(2).Using properties of the shape of the support of P and Q,and how this shape varies under certain automorhisms,we prove B ≠2p for any prime p.We also prove that B = 16 if and only if a certain Abel differential equation of the second type has a polynomial solution.