Quadratic Chabauty for Atkin–Lehner quotients of modular curves of prime level and genus 4, 5, 6

We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus 4, 5, and 6. We find that the only such cu