A catalyst lowers $E_a$ of a reaction from $80$ to $50\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ with no change in the pre-exponential factor ($R=8.314\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$). Select all correct statements.

1. AAt $300\mathrm{K}$ the catalysed rate constant is more than $10^5$ times the uncatalysed one.
2. BThe rate enhancement factor at $600\mathrm{K}$ is larger than at $300\mathrm{K}$.
3. CThe equilibrium constant of the reaction increases because the forward rate increases.
4. DThe rate enhancement factor at $600\mathrm{K}$ is smaller than at $300\mathrm{K}$.