That was my leasing company's prerequisite for me having an aquarium in the first place, so that's done. I've also been looking at structural engineering materials, and I clearly wasn't calculating things correctly.
Based on (https://www.linsgroup.com/MECHANICAL_DESIGN/Beam/beam_formula.htm) those formulas and considering the 4 ft of width of the tank (so the force per linear foot is 425 lbs when including dead load)
I'm looking at a maximum shear force of around 782.6 lbs with the tank up against the wall and a maximum moment of 720.53 lbs*ft, which corresponds to 84.6 PSI compared to the joist's limit of 135 PSI, which is a safety factor of 1.596.
