I installed a tankless water heater that needs 58A, what is the correct double pole circuit breaker for this application?
The correct breaker depends on the size of wire which connects from the panel to the water heater.
Is the wire heavy enough for the full capacity of the heater? For 58 amps residential (which implies the heater will not run full power for more than 2–3 hours), you can use wire rated for 60 amps. If it is likely the heater will run full power for longer than 3 hours, then you need wire capacity for at least 72.5 amps (80% derating).
In solid core copper romex, it needs 4 AWG for the former and 3 AWG for the latter. (For aluminum, it needs heavier wire than copper.)
4 AWG uses up to a 70 amp breaker and 3 AWG requires not more than an 80 amp breaker. A smaller breaker can be used for additional wire safety, but to reduce nuisance tripping, a little headroom above 58 amps, like 65 amps, is a good idea.