INTERNATIONAL JOURNAL OF NUMBER THEORY, v.17, no.04, pp.827 - 842
Abstract
Let E/F be an elliptic curve defined over a number field F. Suppose that E has complex multiplication over (F) over bar, i.e. End((F) over bar)(E) circle times Q is an imaginary quadratic field. With the aid of CM theory, we find elliptic curves whose quadratic twists have a constant root number.