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ON THE TORSION OF ELLIPTIC CURVES OVER QUARTIC NUMBER FIELDS

Published online by Cambridge University Press:  18 August 2006

DAEYEOL JEON ,
CHANG HEON KIM  and
EUISUNG PARK
DAEYEOL JEON
Affiliation:
Department of Mathematics Education, Kongju National University, 182 Shinkwan-dong, Kongju, Chungnam, 314-701, [email protected]
CHANG HEON KIM
Affiliation:
Department of Mathematics, Seoul Women's University, 126 Kongnung 2-dong, Nowon-gu, Seoul, 139-774, [email protected]
EUISUNG PARK
Affiliation:
Korea Institute for Advanced Study (KIAS), 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, [email protected]
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Abstract

We determine which groups ${\mathbb{Z}}/M{\mathbb{Z}}\oplus{\mathbb{Z}}/N{\mathbb{Z}}$ occur infinitely often as torsion groups $E(K)_{\operatorname{tors}}$ when $K$ varies over all quartic number fields and $E$ varies over all elliptic curves over $K$.

Keywords

11G0511G1811G30
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 1 - 12
Copyright
The London Mathematical Society 2006

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