Molecular R-matrix with pseudostate calculations are reported for the electron-impact ionization cross section of the carbon dimer anion. A (1)Sigma_(g)(+) resonance is found near the detachment threshold and two further resonances, of (3)Pi_(g) and (1)Pi_(g) symmetry, are found near 10 eV close to the structures observed experimentally. These unusual shape resonances are a result of the competition between the repulsive Coulomb interaction and the large, attractive polarizability of C2-. Use of the Born approximation to allow for higher partial waves gives a total cross section close to that observed experimentally.