It would be rare for students to take call from home. You should certainly check with your school.
The most common situation is for students to stay at the hospital for the duration of their on-call period. Some schools require full overnight call on every rotation, others may not have any on-call requirements. Sometimes only certain rotations will have on-call requirements. Sometimes being "on-call" means that you only stay until 8 or 10pm and then get to go home - your resident may even send you home early if nothing is happening.
Even if you are allowed to take call from home, if you live 45 minutes away, it's probably best that you just stay at the hospital on those nights if you actually want to be a part of the proceedings. Unless it's an institutional thing, I can't imagine many residents are going to be calling you up in the middle of the night and then waiting the 45 minutes to an hour it's going to take for you to come in to involve in the case.