Equations and rational points of the modular curves X0+ (p)

Let p be an odd prime number and let X-0(+) (p) be the quotient of the classical modular curve X-0 (p) by the action of the Atkin-Lehner operator omega(p). In this paper, we show how to compute explicit equations for the canonical model of X-0(+) (p). Then we show how to compute the modular parametrization, when it exists, from X-0(+) (p) to an isogeny factor E of dimension 1 of its Jacobian J(0)(+) (p). Finally, we show how to use this map to determine the rational points on X-0(+) (p) up to a large fixed height.