The ratios R_2k of renormalized coupling constants g_2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λφ^4 field theory (3D Ising model) within the pseudo-epsilon expansion approach. Pseudo-epsilon expansions for the critical values of g_6, g_8, g_10, R_6 = g_6/g_4^2, R_8 = g_8/g_4^3 and R_10 = g_10/g_4^4 originating from the five-loop renormalization group (RG) series are derived. Pseudo-epsilon expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé–Borel–Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R∗_6 = 1.6488 and R∗_6 = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-epsilon expansions is less favorable. Nevertheless, the conform-B