Shimura Curve Quotients with Odd Jacobians Original Research Article

We study local diophantine properties of Atkin–Lehner quotients of Shimura curves, using the Cerednik–Drinfeld p-adic uniformization of Shimura curves. Applying these diophantine results with recent work of Poonen and Stoll, we show when the Cassels–Tate pairing on the Shafarevich–Tate group of the jacobians of these quotients fails to be alternating.