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Exceptional elliptic curves over quartic fields (CROSBI ID 182123)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Najman, Filip Exceptional elliptic curves over quartic fields // International Journal of Number Theory, 8 (2012), 5; 1231-1246. doi: 10.1142/S1793042112500716

Podaci o odgovornosti

Najman, Filip

engleski

Exceptional elliptic curves over quartic fields

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.

Torsion Group ; Elliptic Curves ; 2-descent

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Podaci o izdanju

8 (5)

2012.

1231-1246

objavljeno

1793-0421

1793-7310

10.1142/S1793042112500716

Povezanost rada

Matematika

Poveznice
Indeksiranost