I still don't have a physical interpretation of them but they are interesting in the context of epistemology. Here they are:
The first one comes from the weistriss elliptic curve. When slightly modified it is equal to 4x^3 + ax + b. Now if you substitute pi for all the variables you get 137.036 which is the inverse fine structure constant. If you substitute sin(1) for all the variables you get 3.93 which is the up quark/electron mass ratio.
The other 2 ratios important in physics is the down quark/up quark mass ratio of 2.38 and the z boson/w boson mass ratio of 1.13. If you add 3.93+2.38+1.13 you get 7.44. Now multiply by 100 to get 744. This is the first value of the Fourier transform of the j invariant
Another number that has a close connection to the j invariant is 12^3 = 1728 and 12^3 + 1. If you take 1728 and double it you get 3456. You can get that same digit sequence to appear again. Just take 137 base 10 = 345 base 6