Go to the Ruger web site and you will find a scope ring chart. I just bought a 77/44 also and found it needs "high" rings or at least that's what comes with the gun from the factory, and what I needed for mounting a Leupold 4X to clear the folded down rear open sight. On the 77/44 both rings are identical in height unlike the 77 rifles and Hawkeyes.
I can't wait to shoot mine! I got a blued/walnut, second year 1998.