We carry out extensive molecular dynamics simulations in order to evaluate the thermodynamic equation of state of the extended simple point charge model of water (customarily described by the acronym SPC/E) over a wide range of temperature and density, with emphasis on the supercooled region. We thereby determine the location of the temperature of maximum density (TMD) line and the liquid spinodal line. In particular, we find that the experimental TMD line lies between the TMD lines of the SPC/E and ST2 models of water, so perhaps the behavior of these two models of simulated water ''bracket'' the behavior of real water. As temperature decreases, we find (i) that maxima appear in isotherms of the isothermal compressibility as a function of density, (ii) that isotherms of the internal energy as a function of volume display negative curvature and (iii) that the pressure of the liquid-vapor spinodal decreases. We compare the results to corresponding behavior found from simulations of the ST2 model of water and find that the behavior of SPC/E, when shifted to higher values of temperature and pressure (Delta P approximate to 50 MPa and Delta T approximate to 80 K) approximates that of ST2. We discuss the implications of our results for the hypothesis that a critical point occurs in the phase diagram of supercooled water. Finally, we argue that the results of our simulations are not inconsistent with the possibility that C' exists for SPC/E water. (C) 1997 American Institute of Physics.