The splitting of primes in division fields of elliptic curves

dc.creatorDuke, William
dc.creatorToth, Arpad
dc.date2001-03-24
dc.date.accessioned2026-07-07T04:40:44Z
dc.date.available2026-07-07T04:40:44Z
dc.descriptionIn 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.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0103151
dc.identifierhttp://arxiv.org/abs/math/0103151
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61128
dc.subjectNumber Theory
dc.titleThe splitting of primes in division fields of elliptic curves
dc.typetext

Files

Collections