The correlations between the maximum mass of neutron stars (NSs) with the properties of nuclear matter at saturation density $$\rho _0$$

ρ_{0}

, i.e., the incompressibility $$K_0$$

K_{0}

, the symmetry energy $$E_{{\textrm{sym}}}(\rho _0$$

E_{sym} (ρ_{0}

), and its slope $$L(\rho _0)$$

L (ρ_{0})

, the isoscalar effective mass $$m^*_{s0}$$

m_{s 0}^{*}

, and the parameter $$f_I$$

f_{I}

, have been investigated using several sets of Skyrme interactions based on the momentum-dependent (MD) Skyrme interactions SAMi-J27 (soft), SAMi-J31 (stiff), and SAMi-J35 (super-stiff), as well as the momentum-independent (MI) Skyrme interaction SkT5. Only one physical quantity is varied at a time for a given set of Skyrme interactions. It is found that the maximum mass of NSs has (1) a strong positive linear correlation with $$K_0$$

K_{0}

for stiff and super-stiff equation of state (EOS) and no correlation with $$K_0$$

K_{0}

for soft EOS; (2) a negative logarithm correlation with the symmetry energy $$E_{{\textrm{sym}}}(\rho _0$$

E_{sym} (ρ_{0}

) for all the EOSs; (3) a positive logarithm correlation with the slope $$L(\rho _0)$$

L (ρ_{0})

for all the EOSs; (4) a positive logarithm correlation with the parameter $$f_I$$

f_{I}

for MD EOS; (5) a negative power-law correlation with $$m_{s0}^*$$

m_{s 0}^{*}

for MD EOS. Based on these established correlations, the constraints to the nuclear matter properties from the mass of PSR J0740+6620 and GW190814 are investigated. Furthermore, we find that while rotation enhances the maximum mass of NSs, it does not effect the underlying correlations between the maximum mass and the aforementioned nuclear matter parameters.

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