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

DOI:
https://doi.org/10.1090/S0025-5718-97-00779-5

MathSciNet review:
1370855

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a family of infinitely many elliptic curves over with a nontrivial rational 2-torsion point and with rank 6, which is parametrized by the rational points of an elliptic curve of rank 1.

**1.**T. J. Kretschmer,*Construction of elliptic curves with large rank*, Math. Comp.**46**(1986), 627-635. MR**87g:11069****2.**B. Mazur,*Rational points on modular curves,*Lecture Notes in Math.**601**(1977), 107-148. MR**56:8579****3.**J. -F. Mestre,*Rang de courbes elliptiques d'invariant donné*, C. R. Acad. Sci.**314**(1992), 919-922. MR**93e:11075****4.**L. J. Mordell,*Diophantine equations*, Academic Press, London, 1969. MR**40:2600****5.**J. H. Silverman,*The arithmetic theory of elliptic curves*, Graduate Texts in Math.**106**, Springer-Verlag, New-York, 1986. MR**87g:11070****6.**H. G. Zimmer and U. Schneiders,*The rank of elliptic curves upon quadratic extension*, in*Computational Number Theory*(eds. A. Pethö, M. E. Pohst, H. C. Williams, H. G. Zimmer), Walter de Gruyter, Berlin, 1991, pp.239-260. MR**92m:11053****7.**H. G. Zimmer,*Computational aspects of the theory of elliptic curves*, in*Number theory and applications*(ed. R. A. Mollin), Kluwer Academic Publishers, Dordrecht, 1989, pp.279-324. MR**92g:11057**

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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:
https://doi.org/10.1090/S0025-5718-97-00779-5

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