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Families of elliptic curves over cubic number fields with prescribed torsion subgroups


Authors: Daeyeol Jeon, Chang Heon Kim and Yoonjin Lee
Journal: Math. Comp. 80 (2011), 579-591
MSC (2010): Primary 11G05; Secondary 11G18
DOI: https://doi.org/10.1090/S0025-5718-10-02369-0
Published electronically: May 12, 2010
MathSciNet review: 2728995
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Abstract: In this paper we construct infinite families of elliptic curves with given torsion group structures over cubic number fields. This result provides explicit examples of the theoretical result recently developed by the first two authors and A. Schweizer; they determined all the group structures which occur infinitely often as the torsion of elliptic curves over cubic number fields. In fact, this paper presents an efficient way of constructing such families of elliptic curves with prescribed torsion group structures over cubic number fields.


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Additional Information

Daeyeol Jeon
Affiliation: Department of Mathematics Education, Kongju National University, Kongju, Chungnam, South Korea
Email: dyjeon@kongju.ac.kr

Chang Heon Kim
Affiliation: Department of Mathematics, Hanyang University, Seoul, South Korea
Email: chhkim@hanyang.ac.kr

Yoonjin Lee
Affiliation: Department of Mathematics, Ewha Womans University, Seoul, South Korea
Email: yoonjinl@ewha.ac.kr

DOI: https://doi.org/10.1090/S0025-5718-10-02369-0
Keywords: Elliptic curve, torsion, cubic number field, modular curve.
Received by editor(s): May 22, 2009
Received by editor(s) in revised form: October 3, 2009
Published electronically: May 12, 2010
Additional Notes: The first named author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No. 20090060674)
The second named author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 20090063182)
The third named author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 20090093827)
Article copyright: © Copyright 2010 American Mathematical Society