scholarly journals Root numbers and parity of ranks of elliptic curves

2011 ◽  
Vol 2011 (658) ◽  
Author(s):  
Tim Dokchitser ◽  
Vladimir Dokchitser
Keyword(s):  
Elliptic Curves ◽  
Root Numbers

On elliptic curves with complex multiplication and root numbers

2020 ◽  
pp. 1-16
Author(s):  
Wan Lee ◽  
Myungjun Yu
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Number Field ◽  
Quadratic Field ◽  
Complex Multiplication ◽  
Imaginary Quadratic Field ◽  
Root Number ◽  
Root Numbers ◽  
Quadratic Twists

Let [Formula: see text] be an elliptic curve defined over a number field [Formula: see text]. Suppose that [Formula: see text] has complex multiplication over [Formula: see text], i.e. [Formula: see text] is an imaginary quadratic field. With the aid of CM theory, we find elliptic curves whose quadratic twists have a constant root number.

Calculating root numbers of elliptic curves over Q

1994 ◽  
Vol 82 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Ian Connell
Keyword(s):  
Elliptic Curves ◽  
Root Numbers
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