5-Torsion in the Shafarevich–Tate Group of a Family of Elliptic Curves
We compute the φ-Selmer group for a family of elliptic curves, where φ is an isogeny of degree 5, then find a practical formula for the Cassels–Tate pairing on the φ-Selmer groups and use it to show that a particular family of elliptic curves have non-trivial 5-torsion in their Shafarevich–Tate grou...
Gespeichert in:
| Veröffentlicht in: | Journal of number theory 2000-05, Vol.82 (1), p.25-46 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | We compute the φ-Selmer group for a family of elliptic curves, where φ is an isogeny of degree 5, then find a practical formula for the Cassels–Tate pairing on the φ-Selmer groups and use it to show that a particular family of elliptic curves have non-trivial 5-torsion in their Shafarevich–Tate group. |
|---|---|
| ISSN: | 0022-314X 1096-1658 |
| DOI: | 10.1006/jnth.1999.2493 |