We have measured the proton elliptic flow excitation function for the Au Au system spanning the beam energy range (2-8)A GeV. The excitation functio
n shows a transition from negative to positive elliptic flow at a beam ener
gy, E-tr similar to 4A GeV. Detailed comparisons with calculations from a r
elativistic Boltzmann equation are presented. The comparisons suggest a sof
tening of the nuclear equation of state from a stiff form (K similar to 380
MeV) at low beam energies (E-beam less than or equal to 2A GeV) to a softe
r form (K similar to 210 MeV) at higher energies (E-beam 4A GeV) where the
calculated baryon density rho similar to 4 rho(0).