An Algorithm for Determining Torsion Growth of Elliptic Curves
We present a fast algorithm that takes as input an elliptic curve defined over Q and an integer d and returns all the number fields K of degree d' dividing d such that E(K)tors contains E(F)tors as a proper subgroup, for all F⊈K. We ran this algorithm on all elliptic curves of conductor less th...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/710748 |
| Acceso en línea: | http://hdl.handle.net/10486/710748 https://dx.doi.org/10.1080/10586458.2020.1771638 |
| Access Level: | acceso abierto |
| Palabra clave: | Elliptic curves torsion over number fields Matemáticas |
| Sumario: | We present a fast algorithm that takes as input an elliptic curve defined over Q and an integer d and returns all the number fields K of degree d' dividing d such that E(K)tors contains E(F)tors as a proper subgroup, for all F⊈K. We ran this algorithm on all elliptic curves of conductor less than 400.000 (a total of 2.483.649 curves) and all d≤23 and collected various interesting data. In particular, we find a degree 6 sporadic point on X1(4,12), which is so far the lowest known degree a sporadic point on X1(m,n), for m≥2 |
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