The selmer groups of elliptic curves and the ideal class groups of quadratic fields

1997 ◽  
Vol 25 (7) ◽  
pp. 2157-2167
Author(s):  
Yen-Mei J. Chen
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Selmer Groups ◽  
Ideal Class ◽  
Class Groups ◽  
Ideal Class Groups ◽  
The Ideal

scholarly journals The Selmer groups and the ambiguous ideal class groups of cubic fields

1996 ◽  
Vol 54 (2) ◽  
pp. 267-274
Author(s):  
Yen-Mei J. Chen
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Upper Bound ◽  
Selmer Groups ◽  
Ideal Class ◽  
Selmer Group ◽  
Class Groups ◽  
Ideal Class Groups ◽  
Cubic Fields ◽  
Rational Isogeny

In this paper, we study a family of elliptic curves with CM by which also admits a ℚ-rational isogeny of degree 3. We find a relation between the Selmer groups of the elliptic curves and the ambiguous ideal class groups of certain cubic fields. We also find some bounds for the dimension of the 3-Selmer group over ℚ, whose upper bound is also an upper bound of the rank of the elliptic curve.

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