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We investigate stable operations in supersingular elliptic cohomology usingisogenies of supersingular elliptic curves over finite fields. Our main resultsprovide a framework in which we give a conceptually simple proof of an ellipticcohomology version of the Morava change of rings theorem and also gives modelsfor explicit stable operations in terms of isogenies and morphisms in certainenlarged isogeny categories. We relate our work to that of G. Robert on theHecke algebra structure of the ring of supersingular modular forms.

Isogenies of supersingular elliptic curves over finite fields and operations in elliptic cohomology