For controllable generation of an isolated attosecond relativistic electron bunch [relativistic electron mirror (REM)] with nearly solid-state density, we proposed [V. V. Kulagin, Phys. Rev. Lett. 99, 124801 (2007)] to use a solid nanofilm illuminated normally by an ultraintense femtosecond laser pulse having a sharp rising edge (nonadiabatic laser pulse). In this paper, the REM characteristics are investigated in a regular way for a wide range of parameters. With the help of two-dimensional (2D) particle-in-cell (PIC) simulations, it is shown that, in spite of Coulomb forces, all of the electrons in the laser spot can be synchronously accelerated to ultrarelativistic velocities by the first half-cycle of the field, which has large enough amplitude. For the process of the REM generation, we also verify a self-consistent one-dimensional theory, which we developed earlier (cited above) and which takes into account Coulomb forces, radiation of the electrons, and laser amplitude depletion. This theory shows a good agreement with the results of the 2D PIC simulations. Finally, the scaling of the REM dynamical parameters with the field amplitude and the nanofilm thickness is analyzed.