In mathematics, the moduli stack of elliptic curves is an algebraic stack classifying elliptic curves. In particular its points with values in some field correspond to elliptic curves over the field, and more generally morphisms from a scheme S to it correspond to elliptic curves over S.
The moduli stack of elliptic curves is denoted by Mell or by M1,1, which is a special case of the moduli stack Mg,n of genus g curves with n marked points.
The moduli stack of elliptic curves is a smooth separated Deligne–Mumford stack of finite type over Spec(Z), but is not a scheme as elliptic curves have non-trivial automorphisms.
There is a proper morphism of M1,1 to the affine line, given by the j-invariant of an elliptic curve, which makes the affine line into the coarse moduli space of M1,1.