A search for high rank congruent number elliptic curves
In this article, we describe a method for flnding congruent num- ber elliptic curves with high ranks. The method involves an algorithm based on the Monsky's formula for computing 2-Selmer rank of con- gruent 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 flnd some new congruent number elliptic curves with rank 6.
Published in 2009.