Hauteur de Faltings de quotients de J0(N), discriminants d'algèbres de Hecke et congruences entre formes modulaires

In this paper we compute the Faltings height of the Jacobian of the modular curve J₀(N). We explain how it is related to the discriminant of the Hecke algebra. This discriminant measures congruences between modular forms. As a corollary we obtain a lower bound for this discriminant. The Faltings height of a quotient A of J₀(N) is also computed.