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Let $p$ be an odd prime number and let $X_0^+(p)$ be the quotient of theclassical modular curve $X_0(p)$ by the action of the Atkin-Lehner operator$w_p$. In this paper we show how to compute explicit equations for thecanonical model of $X_0^+(p)$. Then we show how to compute the modularparametrization, when it exists, from $X_0^+(p)$ to an isogeny factor $E$ ofdimension 1 of its jacobian $J_0^+(p)$. Finally we show how use this map todetermine the rational points on $X_0^+(p)$ up to a large fixed height.

Equations and Rational Points of the Modular Curves $X^+_0(p)$