Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

Elliptic curves, complex multiplication, torsion subgroup, rationals, quadratic fields

Hrčak ID:

259300

URI

https://hrcak.srce.hr/259300

Datum izdavanja:

24.6.2021.

Posjeta: 477 *