Based on the Hugenholtz-Van Hove theorem,six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy t(k),the isospin symmetric and asymmetric parts of the single-nucleon potentials U0(ρ,k)and Usym,i(ρ,k).The six basic quantities include the quadratic symmetry energy Esym,2(ρ),the quartic symmetry energy Esym,4(ρ),their corresponding density slopes L2(ρ)and L4(ρ),and the incompressibility coefficients K2(ρ)and K4(ρ).By using four types of well-known effective nucleon-nucleon interaction models,namely the BGBD,MDI,Skyrme,and Gogny forces,the density-and isospin-dependent proper-ties of these basic quantities are systematically calculated and their values at the saturation density ρ0 are explicitly given.The contributions to these quantities from t(k),U0(ρ,k),and Usym,i(ρ,k)are also analyzed at the normal nuclear density ρ0.It is clearly shown that the first-order asymmetric term U/sym,1(ρ,k)(also known as the symmetry potential in the Lane potential)plays a vital role in deter-mining the density dependence of the quadratic symmetry energy Esym,2(ρ).It is also shown that the contributions from the high-order asymmetric parts of the single-nucleon potentials(Usym,i(ρ,k)with i＞1)cannot be neglected in the calculations of the other five basic quantities.Moreover,by analyzing the properties of asymmetric nuclear matter at the exact saturation density ρsat(δ),the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation Ksat,2 = K2(ρ0)-4.14L2(ρ0).