In this article, we use reductions of the Drinfeld modular curves \(X_{0}(n)\) to obtain curves over finite fields \({\mathbb {F}}_{q}\) of a given genus with many \({\mathbb {F}}_{q}\) -rational points. The main idea is to divide the Drinfeld modular curves by an Atkin–Lehner involution, which has many fixed points to obtain a quotient with a better \(\frac{\#\lbrace \text {rational points}\rbrace }{\text {genus}}\) ratio. If we divide the Drinfeld modular curve \(X_{0}(n)\) by an involution W, then the number of rational points of the quotient curve \(W\backslash X_{0}(n)\) is not less than half of the original number. On the other hand, if this involution has many fixed points, then by the Hurwitz genus formula, the genus of the curve \(W\backslash X_{0}(n)\) is much less than half of the \(g(X_{0}(n))\) .
