Conrad, BrianDiamond, FredTaylor, Richard L.2010-01-251999Conrad, Brian, Fred Diamond, and Richard L. Taylor. 1999. Modularity of certain potentially Barsotti-Tate Galois representations. Journal of the American Mathematical Society 12: 521-567.0894-03471088-6834http://nrs.harvard.edu/urn-3:HUL.InstRepos:3579185We show that certain potentially semistable lifts of modular modrepresentations are themselves modular. As a result we show that any elliptic curve over the rational numbers with conductor not divisible by 27 is modular.en-USJournal Article2010-01-2510.1090/S0894-0347-99-00287-8