Motorcycle Insurance Allstate

Couple questions on motorcycle insurance?
So I recently just bought a motorcycle 07 Yamaha R6S. I’m 19 years old and first time rider. I financed the bike under my name. My parents have Allstate and I’m under there insurance for the car insurance. Can they add a motorcycle under their insurance or do I have to go on my own? If so, how much is full coverage on a bike for a 19 year old? I have 1 ticket on record. Would I be able to just get liability? I live in California. Any advice would be helpful.
They can add youe bike to your parents insurance just give them a call and ask for an estimate on how much more it would cost or you can shop around for a better price. I personally found progressive to be cheap. Idk if you can have just liability but since they didn’t make you get insurance before taking the bike I’m sure you can. I was 20 when I first got my honda 750 about a year ago and it was a one time payment of $150 to cover a full year for liability.
