We report a computer simulation study of the glass transition for water using the extended simple point charge potential. To mimic the difference between standard and hyperquenched glass, we generate glassy configurations with different cooling rates, and we calculate the temperature dependence of the specific heat on heating. The absence of crystallization phenomena allows us, for properly annealed samples, to detect in the specific heat the simultaneous presence of a weak prepeak ("shadow transition") and an intense glass transition peak at higher temperature. Our results support the view-point that the glass transition temperature is higher than the conventionally accepted value 136 K. We also compare our simulation results with the Tool-Narayanaswamy-Moynihan phenomenological model.