Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.8

A Search for High Rank Congruent Number Elliptic Curves


Andrej Dujella
Department of Mathematics
University of Zagreb
Bijenička cesta 30
10000 Zagreb
Croatia

Ali S. Janfada and Sajad Salami
Department of Mathematics
University of Urmia
P.O. Box 165
Urmia
Iran

Abstract:

In this article, we describe a method for finding congruent number elliptic curves with high ranks. The method involves an algorithm based on the Monsky's formula for computing 2-Selmer rank of congruent number elliptic curves, and Mestre-Nagao's sum which is used in sieving curves with potentially large ranks. We apply this method for positive squarefree integers in two families of congruent numbers and find some new congruent number elliptic curves with rank 6.


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(Concerned with sequences A003273 A006991 A062693 A062694 A062695.)

Received April 5 2009; revised version received July 14 2009. Published in Journal of Integer Sequences, July 16 2009.


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