Finding the isotherm with given minima
Using Mathematica, I obtained $T=546 K$, as follows.  One of the nice things about using Mathematica for physical calculations is that it has the ability to understand/keep track of/cancel out/convert units.

The volume is non-physically small -- about 750,000 x smaller than what we'd expect for a mole of, say, ideal gas at $P=100 Pa, T = 546 K$).  One does expect a non-physically small volume, since this is at a non-physically low point on the isotherm, but I would not have predicted it would be this much smaller.

If you were doing it by hand, you'd probably want to use a different approach: