Rational points on $X_0^{+}(125)$

Abstract

We compute the rational points on the Atkin-Lehner quotient $X_0^{+}(125)$ using the quadratic Chabauty method. Our work completes the study of exceptional rational points on the curves $X_0^{+}(N)$ of genus between 2 and 6. Together with the work of several authors, this completes the proof of a conjecture of Galbraith.

8 pages; minor changes following referee report