Very slightly rounded, 11/64" is 0.1719" and is listed in Zeus Charts as 0.1719.
No 40 tpi ME threads are listed as 11/64
None of the figures quoted match BA or BSP.
So it may well be a "Special" 11/64 x 40 tpi., exclusive to the Coventry Die Head
What is the thread form? 55 degrees is Whit, which is what I would feel inclined to expect, but if it is a special it could be different.
Howard