Absolute minimum is graphics card that supports shader model 4.0 (aka DX10) and 64-bit CPU and OS (for editor, UE4 still can build games for 32-bit), UE4 will run on such hardware, it’s only matter how fast it runs.
I runned UE4 on Core2Quad Q9300 and GF9600GT and 4gb ram, using was not plesent but was enouth to see result of C++ coding and unlit mobile games actuly run 60FPS, atleast first versions, empty level run around 30FPS, i somewhat run shooter demo in first verison of UE4 but later demos became unplayably slow.
So yes i think should run on your hardware but rether slow… UE4 is free now so why you asking insted of just trying? ;p