Taylor, RichardLe hung, Bao Viet2014-06-062014-06-062014Le hung, Bao Viet. 2014. Modularity of some elliptic curves over totally real fields. Doctoral dissertation, Harvard University.http://dissertations.umi.com/gsas.harvard:11464http://nrs.harvard.edu/urn-3:HUL.InstRepos:12269826In this thesis, we investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular j-invariants. By analyzing quadratic points on some modular curves, we show that all elliptic curves over certain real quadratic fields are modular.en-USMathematicsNumber TheoryThesis or Dissertation2014-06-06