The energies of isomers of C20 including neutral and positively charged ring, fused ring, flake, and fullerene structures have been calculated within the pseudopotential local density approximation (LDA). The objective is to predict the relative energies of the isomers as well as to validate LDA calculations for the carbon system. For C20, high-level coupled-cluster (CCSD(T)) calculations are just possible and are used for comparison. Our most accurate LDA calculations agree with prior calculations quantitatively and remarkably well with extrapolated CCSD(T) calculations. However, various approximations can qualitatively affect the results. For example softening the pseudopotential for carbon can cause the ordering of the isomer stability to reverse even though good agreement with smaller systems is retained. Similar problems can occur if the plane-wave basis is not sufficiently large.