Resonance impedance matching Colpitts oscillator

[dotm]

Hi.
This is not about any particular project, i just need to understand that.
Given a colpitts oscillator in emitter-configuration like:
http://www.electronics-tutorials.ws/oscillator/osc13.gif
You clearly see that the collector is AC-coupled by that choke, so the Inductor gets a zeropointsymmetrical Signal, thus the phase shift in C2 will occur.

Now imagine that oscillator as quadrupole view, having an amplifier-quadrupole without any particular specifications and the resonance circuit as feedback-quadrupole.

So now in resonant condition, what is the input impedance of the feedback-quadrupole? Is it just the (pure real) resonance resistance  of the tank? Or is it transformed by the capacitive divider somehow? I see that the resonance resistance is transformed towards the output impedance to match the transconductance G_m.

Lets say you'd have an output impedance of your amplifier quadrupole Z₁ which will of course be way smaller than the the resonant resistance, wouldn't it be useful to add a matching network so that the input impedance of the feedback-quadrupole Z₁'  matches  Z₁  ?

I hope i could express myself clearly with my clumsy english...