(2014-06-06) Le hung, Bao Viet; Taylor, Richard; Gross, Benedict; Kisin, Mark
In 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.
