### Rational points on ${X}_{0}^{+}\left(N\right)$ and quadratic $\mathbb{Q}$-curves

Steven D. Galbraith (2002)

Journal de théorie des nombres de Bordeaux

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The rational points on ${X}_{0}\left(N\right)/{W}_{N}$ in the case where $N$ is a composite number are considered. A computational study of some of the cases not covered by the results of Momose is given. Exceptional rational points are found in the cases $N=91$ and $N=125$ and the $j$-invariants of the corresponding quadratic $\mathbb{Q}$-curves are exhibited.