Mine are medium. I've since swapped this one out for the enhanced F1 and the tube length between the scope bell and turrets on the enhanced ATACR is shorter, but I'm still using my medium rings with it. If I get a chance ill try to post a picture with the enhanced one.
I have NF 1.125" Ultralite rings on my BEAST (Same Objective size as 56mm ATACR) with a #3 Bartlien barrel and a 15MOA base. I just barely clear with the NF provided scope caps. You certainly couldn't go any less and slightly higher rings would let you clean better under the scope- more like what is shown in the previous post's photo.
Nightforce calls their 1.125" rings high so you might want to check the height based on brand as it may vary. (I would not think most brands would call these high)