scholarly journals Torsion subgroups of rational elliptic curves over the compositum of all cubic fields

2017 ◽  
Vol 87 (309) ◽  
pp. 425-458 ◽  
Author(s):  
Harris B. Daniels ◽  
Álvaro Lozano-Robledo ◽  
Filip Najman ◽  
Andrew V. Sutherland
Keyword(s):  
Elliptic Curves ◽  
Cubic Fields ◽  
Torsion Subgroups

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

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 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 On class numbers, torsion subgroups, and quadratic twists of elliptic curves

2021 ◽  
pp. 1
Author(s):  
Talia Blum ◽  
Caroline Choi ◽  
Alexandra Hoey ◽  
Jonas Iskander ◽  
Kaya Lakein ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Class Numbers ◽  
Quadratic Twists ◽  
Torsion Subgroups
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