Amyloid diseases, including Alzheimer's and prion diseases, are each associated with unbranched protein fibrils. Each fibril is made of a particular protein, yet they share common properties. One such property is nucleation-dependent fibril growth. Monomers of amyloid-forming proteins can remain in dissolved form for long periods, before rapidly assembly into fibrils. The lag before growth has been attributed to slow kinetics of formation of a nucleus, on which other molecules can deposit to form the fibril. We have explored the energetics of fibril formation, based on the known molecular structure of a fibril-forming peptide from the yeast prion, Sup35, using both classical and quantum (density functional theory) methods. We find that the energetics of fibril formation for the first three layers are cooperative using both methods. This cooperativity is consistent with the observation that formation of amyloid fibrils involves slow nucleation and faster growth.