Tim here is an easy way to determine which rings will work with your scope and rifle combination using a grade school ruler.
Measure the heights of the ring base and ring itself then add them together. Subtract half of outside dimension of the objective. You're looking for a positive value. If you get a negative value then go up to the next taller ring. You can usually find the dimensions for the bases, rings and objective diameter on the manufacturers website.
[rail height + ring height] - [bell diameter x 0.5]
If the value is positive, then your bell will clear the barrel. You want to keep the scope as low as possible so you can maintain a good cheek weld.
Even with a 44mm objective I bet you can use low rings as long as the barrel is a 6 contour or smaller.