Sort each quantity by whether adding a catalyst changes it.

Changed by a catalyst: Activation energy of the pathway, Rate constant of the forward reaction, Time taken to reach equilibrium

Unchanged by a catalyst: Position of the equilibrium, Enthalpy change of the reaction, Equilibrium constant

A catalyst lowers the barrier, so both rate constants rise and equilibrium arrives sooner. But the reactants and products are unchanged, so $\Delta H$ is fixed, and because both directions speed up equally their ratio, the equilibrium constant, cannot shift.