On Drinfeld Modular Curves with Many Rational Points over Finite Fields

It is known that Drinfeld modular curves can be used to construct asymptotically optimal towers of curves over finite fields. Using reductions of the Drinfeld modular curves X₀(), we try to find individual curves over finite fields with many rational points. The main idea is to divide by an Atkin–Lehner involution which has many fixed points in order to obtain a quotient with a better ratio #{rational points}/genus. In a few cases we can improve the known records of rational points.