RATIONAL POINTS ON X_{0}^{+}(p)

STEVEN D. GALBRAITH

Abstract. We study the rational points on X_{0}^{+}(p) = X_{0}(p)/W_{p}. It is known that there are rational points corresponding to cusps and elliptic curves with complex multiplication (CM). We use computational methods to exhibit exceptional rational points on X_{0}^{+}(p) for p = 73, 103, 137, 191 and 311. We also provide the j-invariants of the corresponding non-CM quadratic ℚ -curves.