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.
Here are the power ratings for your particular range.
POWER / RATINGS
Amp Rating at 208V 40
Amp Rating at 240V 40
KW Rating at 208V 8.3
KW Rating at 240V 11.0
So a 40A circuit would work and a #8 conductor is good for 50A according to 2014 NEC Table 310.15 (B)(16), that makes you good to go. I should warn you though that a standard range circuit installed in any residence in the US is a 50A breaker and a #6 conductor circuit with a NEMA 14-50R receptacle. So you might consider meeting everyone else's standards. That way if you ever upgrade your range or sold the house, it would cause less complications down the road.
A 40A appliance on a dedicated circuit usually needs a breaker of at least 40A and wire gauge to match.