Naslov
Exceptional elliptic curves over quartic fields

Autori
Najman, Filip

Izvornik
International Journal of Number Theory (1793-0421) 8 (2012), 5; 1231-1246

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Torsion Group ; Elliptic Curves ; 2-descent

Sažetak
We study the number of elliptic curves, up to isomorphism, over a fixed quartic field K having a prescribed torsion group T as a subgroup. Let T = Z/mZ * Z/nZ, where m|n, be a torsion group such that the modular curve X_1(m, n) is an elliptic curve. Let K be a number field such that there is a positive and finite number of elliptic curves E over K having T as a subgroup. We call such pairs (T, K) exceptional. It is known that there are only finitely many exceptional pairs when K varies through all quadratic or cubic fields. We prove that when K varies through all quartic fields, there exist infinitely many exceptional pairs when T = Z/14Z or Z/15Z and finitely many otherwise.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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