Neighboring resistances (input & output resistances) play a part in shaping the rolloff curve. Although naturally the obvious factors are LC values and L:C ratio. There are various ways to arrange a bandpass filter. Therefore it becomes difficult to calculate how effects interact to influence behavior.
I have not seen a simple formula for predicting performance. I've found I learn a lot by watching a variety of simulations, applying a sine sweep. A reasonable range of frequencies is from 1/10 to 10x the center frequency. That is likely to reveal the rolloff curve, how sharp it is or how gradual it is.