Modified Colpits

Actually, the transistor is cut off unless the current source can provide current when the voltage across it is negative. This will work fine in a simulation, but you probably won't be able to make a real-world current source work in this circuit unless you return it to a negative voltage.
In that case, you wouldn't need the 50k resistor.
What I'm trying to say is that the inductor is grounding the base at DC. The simplest fix is a cap in series with the inductor.
 
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