The splitting of primes in division fields of elliptic curves
| dc.creator | Duke, William | |
| dc.creator | Toth, Arpad | |
| dc.date | 2001-03-24 | |
| dc.date.accessioned | 2026-07-07T04:40:44Z | |
| dc.date.available | 2026-07-07T04:40:44Z | |
| dc.description | In this paper we will give a global description of the Frobenius for the division fields of an elliptic curve E which is strictly analogous to the cyclotomic case. This is then applied to determine the splitting of a prime p in subfields of such a division field. Such fields include a large class of non-solvable quintic extensions and our application provides an arithmetic counterpart to Klein's "solution" of quintic equations using elliptic functions. A central role is played by the discriminant of the ring of endomorphisms of the elliptic curve reduced modulo p. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0103151 | |
| dc.identifier | http://arxiv.org/abs/math/0103151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61128 | |
| dc.subject | Number Theory | |
| dc.title | The splitting of primes in division fields of elliptic curves | |
| dc.type | text |