You are asking how to analyze this circuit:
Forget about what you think it should be called. Before attempting to model specific aspects, first try to understand the circuit.
The opamp provides gain of -R2/R1. For an ideal opamp, the output of the opamp has zero impedance in this circuit. That means anything between its output and ground, like L1, is irrelevant. That only influences how much current the opamp must source or sink to maintain the output voltage, but has no effect on that output voltage.
Step back and forget you ever heard of a "Hartley oscillator" (I'm not sure this qualifies as one anyway, but that's irrelevant). Instead of trying to figure out what some made-up circuit does, try synthesizing it instead. That will teach you a lot more about the final result.
So, you've got an amplifier with gain below -1. To make an oscillator, you need overall loop gain >1 at the desired oscillating frequency. Therefore, you need a feedback network that inverts at the oscillation frequency. Note that inversion is the same as 180° phase shift. Now actually stop and think how you'd achieve that with passive parts.
You should know by now that a LC high pass filter introduces some phase shift. A simple LC filter might not get the phase shift you need at the gain you need. However, two might more easily. There are various ways to achieve this. You might want to exploit resonance. I'm not going to do this for you because you clearly need to spend some time thinking about what the circuit is really doing qualitatively, instead of jumping straight to some formula that you found in a book somewhere.
We've reduced the problem to making a passive circuit that phase shifts at least some frequency by 180°, while not attenuating the result by more than a particular value. In this case, you have some latitude over the attenuation since you can compensate by increasing the gain of the opamp circuit. But, you can't go too far with that else the inverting opamp amplifier you have won't work as a simple R2/R1 gain anymore. Start with R2/R1 = 20. You really should be able to make a passive phase shifter that attenuates by less than 20.