3 problems

Let $N$ be a positive integer. Let $J_0(N)$ be the Jacobian of the modular curve $X_0(N)$, and let $J_0(N)(\mathbf{Q})_{\mathrm{tors}}$ denote its rational torsion subgroup. Let…

Let $p$ be prime. Let $J_1(p)$ be the Jacobian of the modular curve $X_1(p)$, let $J_1(p)(\mathbf{Q})_{\mathrm{tors}}$ denote its rational torsion subgroup, and let…

Ribet's conjecture. If $\mathfrak{m}$ is an Eisenstein maximal ideal, then