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The symmetry energy obtained with the effective Skyrme energy densityfunctional is related to the values of isoscalar effective mass and isovectoreffective mass, which is also indirectly related to the incompressibility ofsymmetric nuclear matter. In this work, we analyze the values of symmetryenergy and its related nuclear matter parameters in five-dimensional parameterspace by describing the heavy ion collision data, such as isospin diffusiondata at 35 MeV/u and 50 MeV/u, neutron skin of $^{208}$Pb, and tidaldeformability and maximum mass of neutron star. We obtain the parameter setswhich can describe the isospin diffusion, neutron skin, tidal deformability andmaximum mass of neutron star, and give the incompressibility$K_0$=250.23$\pm$20.16 MeV, symmetry energy coefficient $S_0$=31.35$\pm$2.08MeV, the slope of symmetry energy $L$=59.57$\pm$10.06 MeV, isoscalar effectivemass $m_s^*/m$=0.75$\pm$0.05 and quantity related to effective mass splitting$f_I$=0.005$\pm$0.170. At two times normal density, the symmetry energy weobtained is in 35-55 MeV. To reduce the large uncertainties of $f_I$, morecritical works in heavy ion collisions at different beam energies are needed.

Constraints on the symmetry energy and its associated parameters from nuclei to neutron stars