Journal of the Ramanujan Mathematical Society

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Generators for Congruent Number Curves of Ranks at Least Two and Three


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1 College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275–8576, Japan
     

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In this paper, we study generators for the Mordell-Weil groups EN (Q) of congruent number curves EN defined by y2 = x3 − N2x for positive integers N. In fact, we give generators for the rank two and three parts of EN (Q) for infinitely many integers N.
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  • Generators for Congruent Number Curves of Ranks at Least Two and Three

Abstract Views: 229  |  PDF Views: 0

Authors

Yasutsugu Fujita
College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275–8576, Japan

Abstract


In this paper, we study generators for the Mordell-Weil groups EN (Q) of congruent number curves EN defined by y2 = x3 − N2x for positive integers N. In fact, we give generators for the rank two and three parts of EN (Q) for infinitely many integers N.