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http://dx.doi.org/10.5831/HMJ.2010.32.1.177

A METHOD OF COMPUTATIONS OF CONGRUENT NUMBERS AND ELLIPTIC CURVES

Park, Jong-Youll (Department of Mathematics Education, Chonnam National University)
Lee, Heon-Soo (Graduate School, Chonnam National University)

Publication Information

Honam Mathematical Journal / v.32, no.1, 2010 , pp. 177-192 More about this Journal

Abstract

We study the concepts of congruent number problems and elliptic curves. We research the structure of the group of elliptic curves and find out a method of the computation of L( $E_n$ , 1) and L'( $E_n$ , 1) by using SAGE program. In this paper, we obtain the first few congruent numbers for n ${\leq}$ 2500.

Keywords

Congruent number problem; Elliptic curves; Modular form; Birch and Swinnerton-Dyer Conjecture; SAGE program;

Citations & Related Records

Reference

1	J. H. Coates, Congruent Number Problem, Pure and Applied Mathematics Quarterly, Vol.1, No. 1 (2005).
2	A, Dujella, A. S. Janfada, S. Salami, A Search for High Rank Congruent Number Elliptic curves, J. of Integer Sequence, Vol.12 (2009).
3	N, Kohlitz, Introduction to Elliptic Curves and Modular Forms, Springer, (2000).
4	K Rubin. A,Silverberg, Ranks of Elliptic Curves, Bulletin of AMS, Vol.39, No.4 (2002).
5	W. Stein, The Congruenl Number Problem .' A Thousand Year Old Unsolved Problem (http://modular.math.washington.edu).
6	L. C. Washington, Elliptic curves, Number theory and Cryptography, CRC Press, (2003),