You mean resonant peak frequency? It really will vary by pickup, cable capacitance, etc… but according to this
data sheet, it’s about 2.5kHz for P bass.
The resonant peak is formed by the inductance of the pickup(s) and the loading capacitance - which is partly in the pickups themselves (different winding techniques will give different interwinding capacitance), and the rest (usually most of it) in the cable.
Some manufacturers will quote a resonant frequency of the pickup itself (without the cable) - this is
interesting information, but incomplete - the reality is that the peak will be lower in frequency when in use.
If we start with a relatively low capacitance cable - say 600 pF for a 15 footer, Most traditional P pickups will give you a resonance around 2 to 2.2 kHz. A soloed J pickup will land you a bit North of that - 2.2 to 2.4 kHz. Both pickups on with a Jazz bass, and you're at 2.8 to 3 kHz.
When you turn down the volume control(s) (especially on a J), the resonant peak is damped - it doesn't really resonate.
The J scoop has nothing to do with pickups loading each other electrically - it's in the positions of the pickups entirely. It doesn't happen at one frequency - it happens at 4 (or 5, or 6, or) - the scoop is a wavelength phenomenon, and as each string has a different propagation velocity, the frequency at which a give wavelength occurs is different on every string. So if you try to eq out the scoop, you can fix one string, but the other 3 will be even more messed up - it is literally unfixable with one signal path.
A lot of folks talk about
pickups sounding "scooped" - practically speaking, they don't - the "scoop" you hear from different pickups is that the upper mid peak is distracting you, so you hear that rather than the lower mids.