Abstract:  For a finite abelian group A, we define a functor from E_∞-rings to spaces by sending an E_∞-ring R to the space of spectral elliptic curves with derived level A-structures over R. We compute the cotangent complex of this functor. Then we use Lurie’s spectral Artin’s  representability theorem to prove that this functor is representable by a spectral Deligne-Mumford stack.