 A particularly rich source for formal group laws are elliptic curves.A cohomology theory A with 

is called "elliptic" if it is even periodic and its formal group law is isomorphic to a formal group law of an elliptic curve E over R. The usual construction of such elliptic cohomology theories uses the Landweber exact functor theorem.If the formal group law of E is Landweber exact, one can define an elliptic cohomology theory (on finite complexes) by

Franke has identified the condition needed to fulfill Landweber exactness