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In mathematics, the moduli stack of elliptic curves, denoted as M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} or M ell {\displaystyle {\mathcal {M}}_{\textrm {ell}}} , is an algebraic stack over Spec {\displaystyle {\text{Spec}}} classifying elliptic curves. Note that it is a special case of the Moduli stack of algebraic curves M g , n {\displaystyle {\mathcal {M}}_{g,n}}. In particular its points with values in some field correspond to elliptic curves over the field, and more generally morphisms from a scheme S {\displaystyle S} to it correspond to elliptic curves over S {\displaystyle S}. The construction of this space spans over a century because of the various generalizations of elliptic curves as the field has developed. All of these generalizations are contained in M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}}.