[en] The excitation of the J^π;T=1⁺;0 and 1⁺;1 states at E_x=12.71 and 15.11 MeV in ¹²C has been studied at momentum transfers q<0.5 fm^-1 in inelastic electron scattering. The corresponding ground state radiation widths and transition radii for the isoscalar and isovector transition are deduced as Γ_γ0=0.32(2) eV, R_tr=2.95(9) fm and Γ_γ0=35.9(6) eV, R_tr=2.63(4) fm, respectively. For the evaluation of Γ_γ0 and R_tr for the transition to the 15.11 state (e,e'), data of the present work have been combined with older data from other low energy electron accelerators. The results support the strong isospin mixing of the two 1⁺ states, and in the frame of a two-state model a Coulomb matrix element < H_C>=118(8) keV is derived. This value agrees with other experiments using electromagnetic or pionic probes but is much more accurate. Furthermore, the measured difference in the transition radii for the isoscalar and isovector transitions allows for the first time a unique determination of the sign of < H_C>