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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Construction of high-rank elliptic curves
with a nontrivial torsion point


Author: Koh-ichi Nagao
Journal: Math. Comp. 66 (1997), 411-415
MSC (1991): Primary 11G05, 11D25; Secondary 11Y50
MathSciNet review: 1370855
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Abstract: We construct a family of infinitely many elliptic curves over ${\Bbb Q} $ with a nontrivial rational 2-torsion point and with rank $\ge $ 6, which is parametrized by the rational points of an elliptic curve of rank $\ge $ 1.


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Additional Information

Koh-ichi Nagao
Affiliation: Shiga Polytecnic College, 1414 Furukawa Cho, Oh-Mihachiman Shiga 523, Japan
Email: nagao@shiga-pc.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00779-5
PII: S 0025-5718(97)00779-5
Keywords: Elliptic curve
Received by editor(s): June 16, 1994
Received by editor(s) in revised form: November 1, 1994, and November 13, 1995
Article copyright: © Copyright 1997 American Mathematical Society