  We prove, under suitable assumptions, that $p$-torsion Tate-Shafarevich
classes for elliptic curves over the rationals are visible in quotients of
Jacobians of modular curves, as predicted by a conjecture of Jetchev-Stein. The
key ingredient is the non-triviality of the Bertolini-Darmon bipartite
Kolyvagin system, which implies that suitable cohomology classes of the system
form a basis of the Selmer group modulo $p$.
