Op Amp based Colpitts oscillator
The op-amp output is tied to ground and, there is no positive feedback anyway so it wouldn't work. Even if you switched the LC arrangement to give positive feedback there is no non-linear circuit to give gain control - the circuit, when "wired correctly" will alternate between full clipping and hardly anything.

Maybe you were trying to do this one: -



It works because there is positive feedback - the amp inverts (180º shift) and the L and C conspire to produce another 180º at resonance. I can't vouch for it working and I don't think the capacitor C2 will do anything except make it appear like a colpitts oscillator. I found it by googling "op-amp colpitts".

This is a better circuit and you can swap the crystal and series 75pF for an inductor methinks: -



It works better because there are diodes that limit the amplitude and make the circuit stable. It's basically a small variation on the standard emitter follower colpitts circuit.