We have performed the first ab initio computational investigation of the elastic scattering of electrons by the isolated cluster which was described with its symmetry lowered (due to Jahn-Teller distortion) to the C-2 and C-i point groups. The energy range considered was 1-10 eV. The geometry and electronic energy of the molecule were taken to be those of its ground state. The total and partial cross sections were calculated through a coupled-channel dynamics with inclusion of a parameter-free model exchange and correlation-polarization potentials. The scattering process has been found to exhibit a rather complex resonant structure due to the special "hollow" framework of the molecular cage. One distinguishing feature of the cross sections is the presence of strong near-threshold peaks which we attribute to a series of C-20(-) metastable negative ions. The present results therefore provide a benchmark calculation which could be of guidance to future experiments on the very recently produced fullerene C-20 species. In fact, the analysis carried out in the present work allows us to assign each scattering resonance to a specific molecular state, their symmetries and parameters obtained from our calculations.