Rational points on $X^+_0(125)$

Abstract: We compute the rational points on the Atkin-Lehner quotient $X<sup>+_0(125)$ using the quadratic Chabauty method. Our work completes the study of exceptional rational points on the curves $X<sup>+_0(N)$ of genus between 2 and 6. Together with the work of several authors, this completes the proof of a conjecture of Galbraith.