Do you have a frontend loader on your tractor?
If so, let gravity do most of the work
Used the loader to dig an inclined pit about 2/3 the diameter of the culvert about 2 to 2 1/2 ft deep to one side of the pad. Put a couple 10 or 12' 4x's in the excavation as illustrated below.
Roll the culvert as shown so that half 'falls' into the pit and upends on the 4x's.
Use the front end loader to teeter the culvert back to vertical on the 4x's, either by pushing or pulling.
Stick 2 more 4x's under the culvert to to 'bridge' the inclined pit.
If you're worried about the strength of your two original 4x's, teeter the culvert perpendicularly enough to free one and slide it onto the pad, go around to the other side and do the same so you have a total of 4 'bridging' the hole.
All this can be done by hand; the tractor (should) just make it quicker.
As previously advised, I'd try just tilting it up with the tractor first. If it won't pick up one end outright (or with a lever stuck in it), you may be able to incrementally wedge one end up; at a certain point the weight of the culvert will actually help to upend the cylinder.