2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116543Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to w_N-Atkin-Lehner twists of most modular curves X_0(N) and to w_p-Atkin-Lehner twists of certain Shimura curves X^{D+}.9 pagesNumber TheoryAlgebraic Geometrytext