To be safe, I would want to know what the spacing is between joists underneath? What is the sub-floor itself--plywood, pressed board, advantec?
If you know any builders, they might be able to give an educated guess, depending on when the house was built, area, and what the practices were at that time.
If it were me, I'd be ripping up the footprint of the tank and reinforcing it. But I understand your renting and even asking your landlord...they might be like no way, if you did ask them about it.
It's like your putting a mini hot tub in there and liability/building codes, issues like that-the underneath need appropriate reinforcing.
Awesome size tank though!