Exceptional elliptic curves over quartic fields (CROSBI ID 182123)
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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