Let J0(p) be the Jacobian of the modular curve X0(p). The group of connected components of its Néron model is cyclic, and has two special generators. One comes from the cuspidal group, the other from the Shimura subgroup. We compute their ratio, answering a question raised by B. Mazur (Inst. Hautes Etudes Sci. Publ. Math. 47, 1977, 33-186).