  We have measured the proton elliptic flow excitation function for the Au + Au
system spanning the beam energy range 2 -- 8 AGeV. The excitation function
shows a transition from negative to positive elliptic flow at a beam energy,
$E_{tr} \sim$ 4 AGeV. Detailed comparisons with calculations from a
relativistic Boltzmann-equation are presented. The comparisons suggest a
softening of the nuclear equation of state (EOS) from a stiff form (K \sim 380
MeV) at low beam energies (E_{Beam} \le 2 AGeV) to a softer form (K \sim 210
MeV) at higher energies (E_{Beam} \ge $ 4 AGeV) where the calculated baryon
density $ \rho \sim 4 \rho_0$.
