Abstract:
We study the rational points on XO +(p) = XO(p)/Wp. 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 XO +(p) for p = 73, 103, 137, 191 and 311. We also provide the j-invariants of the corresponding non-CM quadratic Q-curves.