Exclusive and kinematically complete high-statistics measurements of the basic double pionic fusion reactions pn -> dpi0pi0, pn -> d pi+pi- and pp -> dpi+pi0 have been carried out simultaneously over the energy region of the ABC effect using the WASA detector setup at COSY. Whereas the isoscalar reaction part given by the dpi0pi0 channel exhibits the ABC effect, i.e. a low-mass enhancement in the pipi-invariant mass distribution, as well as the associated resonance structure in the total cross section, the isovector part given by the dpi+pi0 channel shows a smooth behavior consistent with the conventional t-channel Delta Delta process. The dpi+pi- data are very well reproduced by combining the data for isovector and isoscalar contributions, if the kinematical consequences of the isospin violation due to different masses for charged and neutral pions are taken into account.