Two critical points have been revealed in the normal-state phase diagram of the electron-doped cuprate superconductor Nd2-xCexCuO4 by exploring the Fermi surface properties of high-quality single crystals by high-field magnetotransport. First, the quantitative analysis of the Shubnikov-de Haas effect shows that the weak superlattice potential responsible for the Fermi surface reconstruction in the overdoped regime extrapolates to zero at the doping level xc=0.175 corresponding to the onset of superconductivity. Second, the high-field Hall coefficient exhibits a sharp drop right below optimal doping xopt=0.145 where the superconducting transition temperature is maximum. This drop is most likely caused by the onset of long-range antiferromagnetic ordering. Thus the superconducting dome appears to be pinned by two critical points to the normal state phase diagram.