The basic Colpitts oscillator circuit look like this and you will see some similarities.
If you consider positive feedback is applied to compensate for the losses in the tuned circuit, the amplifier and feedback circuit create a negative resistor. When Z1 and Z2 are capacitive, the impedance across the capacitors can be estimated from a formula I won't lay on you here because it includes beta, hie, as well as XC1 and XC2. Suffice to say it can be shown that the input impedance is a negative resistor in series with C1 and C2. And the frequency is in accordance with:
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