scholarly journals The $2$-class groups of cubic fields and $2$-descents on elliptic curves

1992 ◽  
Vol 44 (4) ◽  
pp. 557-565 ◽  
Author(s):  
Mayumi Kawachi ◽  
Shin Nakano
Keyword(s):  
Elliptic Curves ◽  
Class Groups ◽  
Cubic Fields

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.

scholarly journals Torsion of rational elliptic curves over cubic fields

2016 ◽  
Vol 46 (6) ◽  
pp. 1899-1917 ◽  
Author(s):  
Enrique González-Jiménez ◽  
Filip Najman ◽  
José M. Tornero
Keyword(s):  
Elliptic Curves ◽  
Cubic Fields

scholarly journals Bounds on $2$-torsion in class groups of number fields and integral points on elliptic curves

2020 ◽  
Vol 33 (4) ◽  
pp. 1087-1099 ◽  
Author(s):  
M. Bhargava ◽  
A. Shankar ◽  
T. Taniguchi ◽  
F. Thorne ◽  
J. Tsimerman ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Number Fields ◽  
Class Groups ◽  
Integral Points

Elliptic curves with good reduction everywhere over cubic fields

2015 ◽  
Vol 11 (04) ◽  
pp. 1149-1164 ◽  
Author(s):  
Nao Takeshi
Keyword(s):  
Elliptic Curves ◽  
Infinite Family ◽  
Good Reduction ◽  
Cubic Fields

We give a criterion for cubic fields over which there exist no elliptic curves with good reduction everywhere, and we construct a certain infinite family of cubic fields over which there exist elliptic curves with good reduction everywhere.

scholarly journals On 3-class groups of non-Galois cubic fields

1979 ◽  
Vol 35 (4) ◽  
pp. 395-402 ◽  
Author(s):  
Kiyoaki Iimura
Keyword(s):  
Class Groups ◽  
Cubic Fields
Sign in / Sign up

Export Citation Format

Share Document