Lipid shape and charge are connected with the physical properties and the biological function of membranes. Cardiolipin, a double phospholipid with four chains and the potential of changing its charge with pH, is crucially connected with mitochondrial inner membrane shape, and recent experiments suggest that local pH changes allow highly curved local geometries. Here, we use a coarse-grained molecular dynamics model to investigate the mechanical properties of cardiolipin bilayers, systematically varying the headgroup charge and the composition in mixtures with zwitterionic 1,2-dioleoyl-glycero-3-phosphatidylcholine (DOPC) or 1,2-dioleoyl-glycero-3-phosphatidylethanolamine (DOPE). Low cardiolipin charge, corresponding to low pH, was found to induce bending moduli on the order of kBT and curved microdomains. On the length scale investigated, in contrast to continuum theoretical models, we found the area modulus and bending modulus to be inversely correlated for mixtures of cardiolipin and DOPC/DOPE, explainable by changes in the effective headgroup volume.