What size circuit breaker is required for a GE model JBP68HKWW range?
It depends on the wire going to the range.   

If the wire is 8 AWG you can only use a 40A breaker, regardless of what the range's instructions may tell you.  

If it is 6 AWG, you should use 40A or 50A depending on what the range's instructions say to use.

While you're in there... this is a very good time to make sure you are using the modern, grounded 4-wire connection including a NEMA 14 plug/socket if it uses a plug.  The old 3-wire connection is hazardous, as any problem with the neutral wire will electrify the chassis of the range.  No kidding, and this problem has a body count.   

It's especially a shame if the house is wired with modern /3 cable +ground, but someone downgraded it because their used range had a 3-prong connection.   If it doesn't have a ground now, the rules now allow you to add just a ground wire, either back to the panel or anywhere else with a 10AWG ground wire back to the panel.