LC oscillators are finicky to get going.
It's hard to predict the right component values except in a general way. It depends on the characteristics of the inductor, the transistor, what is proper biasing based on surrounding circuitry, etc.
Then you need to adjust the bias to just the right point, so as to get the transistor operating between a small amount on and a medium amount on.
I've also seen more than one Colpitts configuration. (And more than one Clapp and Hartley types, etc.)
Seems there's not just one proper configuration. The avenue is open for experimentation and improvement.