Not always and a crystal based Colpitts doesn't require and inductor either.A colpit oscillator requires resistor capacitor, transistor and an inductor.
The transistor is bias using voltage divider principle.
The feedback cct is connected to the collector & it require to 2 capacitor in series parallel to an inductor & to the ground.
by Jake Hertz
by Duane Benson
by Aaron Carman
by Duane Benson