TORSION POINTS OF ELLIPTIC CURVES OVER QUADRATIC FIELD

Authors

  • N. Mukhtar Department of Mathematics and Statistics, Nuhu Bamalli Polytechnic, Zaria, Nigeria Author
  • A. T. Imam Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria Author

Keywords:

Quadratic Field, torsion points, Elliptic Curve

Abstract

An elliptic curve is a cubic polynomial in two variables in which there is at least one rational solution. The set of all rational solutions to an elliptic curve is known to be an abelian group which is finitely generated. In this paper, we obtained the 2 – torsion and 3 – torsion points for the family of elliptic curves of the forms ???????? = ???????? + ???????? and ???????? = ???????? + ???????????? + ???????? over quadratic field.

         Views | Downloads: 43 / 33

Downloads

Download data is not yet available.

References

Poincare, H. (1901). Sur les proprieties arithmetique des courbes algebrique. Journal mathematics pure and applied 7.

Nagell, T. (1935). Solution de quelque problemes dans la theorie arithmetique des cubiques planes du premier genre. Wid. Akad. Skrifter Oslo I. Nr.1.(Springer).

Lutz, E. (1937). Sur l’equation ???? 2 = ???? 3 − ???????? − ???? dans les corps p-adic. Journal of Reine Angewandte Mathematik. 177:431–466.

Mazur, B. (1978). Rational isogenies of prime degree. Inventiones Mathematicae. 44, 129–162.

Kenku, M. A. and Momose, F. (1988). Torsion points on elliptic curves defined over quadratic fields. Nagoya mathematics Journal, 125 – 149.

Kamienny, S. (1992). Torsion points on elliptic curves and q – coefficient of modular form. Inventiones Mathematicae Journal, 109, 221 – 229.

Jody, R. and Sophie, D. (2014). Torsion of elliptic curves over quadratic fields. OAlib Journal.

Christian, C. (2006). Torsion points of elliptic curves over number fields. Honors thesis University of Massachusetts.

Silverman, H. J. and Tate, J. (1992). Rational Points on elliptic curves (2nd. ed.). Springer – Verlag, New York.

Downloads

Published

2021-12-01

How to Cite

TORSION POINTS OF ELLIPTIC CURVES OVER QUADRATIC FIELD. (2021). The Transactions of the Nigerian Association of Mathematical Physics, 17, 179–182. https://nampjournals.org.ng/index.php/tnamp/article/view/211

Share

Similar Articles

1-10 of 14

You may also start an advanced similarity search for this article.