I used the medium Burris Signature Zee rings with my viper (part #420588) and the height worked out great. If you like a more tactical look check out the Burris XTR signature zee rings... They come in medium height also and are great set of rings... IMO

I'm sorry but I had the 50mm objective not the 44mm that you mention. You may can go with low rings... I'm not sure on that part number..