Eisenstein ideal

In mathematics, the Eisenstein ideal is an ideal in the endomorphism ring of the Jacobian variety of a modular curve, consisting roughly of elements of the Hecke algebra that annihilate the Eisenstein series. It was introduced by Barry Mazur (1977), in studying the rational points of modular curves. An Eisenstein prime is a prime in the support of the Eisenstein ideal (this has nothing to do with primes in the Eisenstein integers). In mathematics, the Eisenstein ideal is an ideal in the endomorphism ring of the Jacobian variety of a modular curve, consisting roughly of elements of the Hecke algebra that annihilate the Eisenstein series. It was introduced by Barry Mazur (1977), in studying the rational points of modular curves. An Eisenstein prime is a prime in the support of the Eisenstein ideal (this has nothing to do with primes in the Eisenstein integers). Let N be a rational prime, and define