We determine the quadratic points on the modular curves \(X_0(N)\) for \(N\le 100\) for which this has not been previously done, namely the cases \(\begin{aligned} N\in \{66,70,78,82,84,86,87,88,90,96,99\}. \end{aligned}\) We accomplish this by improving on the “going down method,” which uses the fact that we have a moduli description of all the (infinitely many) quadratic points on \(X_0(n)\) for some divisor n of N.
