Electronic – Why is this Op Amp generating a 12kHz signal

I think you have a few issues that you need to address.

The primary issue is that the Q of your tank is very low. The Q of a parallel RLC circuit is:

$$Q=R\sqrt{\frac{C}{L}}$$

Considering that your resistive feedback is effectively in parallel with the tank, we can calculate Q:

$$ 1500\Omega \sqrt{\frac{1nF}{15\mu H}}=Q= 12 $$

The Q of 12 is VERY low, so this is probably your main issue. Increasing the magnitude of R1 and R2 should be sufficient for your circuit to oscillate properly. See my example simulation here. If your Q is too low, you will need more gain to compensate for the losses.

A second potential problem is that the op-amp you selected, the 741, has a bandwidth that is a bit low for the frequency you selected. The datasheet indicates a bandwidth of 1.5 MHz, and your oscillator frequency is 1.3 MHz. This may result in your op-amp not providing enough gain for the oscillator to function properly. There are MANY op-amps that would provide an improvement over a 741.

Another possible issue is that oscillators are a bit tricky to get working in simulators. While it sounds like this is not an issue for you, it is a potential pitfall. Often, the random noise that usually starts oscillators in reality does not occur in a simulator. Often a noise source or impulse is required to kick-start the oscillator.

The way you're checking your circuit is not appropriate. The dark current specified in the datasheet is for 20 V reverse voltage applied. However your circuit does not reverse bias the photodiode.

The datasheet shows typical dark current vs reverse bias:

With no reverse bias, you should expect 0 dark current, as in any other diode with 0 V applied.

You need to test your circuit with some light applied to the photodiode. An input signal on the order of 10 to 100 nW (depending on wavelength) should produce a measurable output signal. Be aware that your photodiode has a strongly directional response, and the input light must be entering from nearly "straight on" to be detected. This will limit your ability to detect diffuse reflections.