Let E/F be an elliptic curve defined over a number field F. Suppose that E has complex multiplication over F¯, i.e. EndF¯(E) ⊗ ℚ is an imaginary quadratic field. With the aid of CM theory, we find elliptic curves whose quadratic twists have a constant root number.

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关于具有复数乘法和根数的椭圆曲线

让乙/F是在数域上定义的椭圆曲线F. 假设乙有复数乘法F¯， IE结尾F¯(乙) ⊗ ℚ是一个虚构的二次场。在CM理论的帮助下，我们找到了二次扭曲具有恒定根数的椭圆曲线。