In mathematics, Ihara's lemma, introduced by and named by , states that the kernel of the sum of the two p-degeneracy maps from J<sub>0</sub>(N)ÃÂJ<sub>0</sub>(N) to J<sub>0</sub>(Np) is Eisenstein whenever the prime p does not divide N. Here J<sub>0</sub>(N) is the Jacobian of the compactification of the modular curve of ÃÂ<sub>0</sub>(N).