Glasnik matematički, Vol. 56 No. 1, 2021.
Original scientific paper
https://doi.org/10.3336/gm.56.1.04
Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields
Enrique González-Jiménez
orcid.org/0000-0002-0469-5431
; Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain
Abstract
In a series of papers we classify the possible torsion structures of rational elliptic curves base-extended to number fields of a fixed degree. In this paper we turn our attention to the question of how the torsion of an elliptic curve with complex multiplication defined over the rationals grows over quadratic fields. We go further and we give an explicit characterization of the quadratic fields where the torsion grows in terms of some invariants attached to the curve.
Keywords
Elliptic curves, complex multiplication, torsion subgroup, rationals, quadratic fields
Hrčak ID:
259300
URI
Publication date:
24.6.2021.
Visits: 516 *