Early Morning Mental Meander

A = 10³, B = 10⁹, C=10²⁷, D=10², E=3, F=4, G=8, H=3, I=5, J=???, K=???, L=11, M=10⁶, N=1, O=1, P=10¹⁸, Q=10¹⁵, R=3, S=6, T=2, U=4, V=5, W=2, X=6, Y=20, Z=???

I woke up and this popped into my head. Two questions:

First, what is the rule?

Second, what are the missing values?

Hint: I excluded the number 0 because, well, it doesn't really count.

First one with the answer gets a star named after him/her.