We calculate the Gaussian curvature modulus of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value /κ = −1.04 ± 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce _m/κ_m ≈ −0.98 ± 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z₀ of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K_0m. By also analyzing the lateral stress profile σ₀(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K_0m and through the first and second moment of σ₀(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.