For an integer $m>1$, it is shown that each congruence class modulo $m$ contains infinitely many congruent numbers whose associated elliptic curves have rank at least two.
@article{1272289544,
author = {Johnstone, Jennifer Ann and Spearman, Blair Kenneth},
title = {On the distribution of congruent numbers},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {86},
number = {1},
year = {2010},
pages = { 89-90},
language = {en},
url = {http://dml.mathdoc.fr/item/1272289544}
}
Johnstone, Jennifer Ann; Spearman, Blair Kenneth. On the distribution of congruent numbers. Proc. Japan Acad. Ser. A Math. Sci., Tome 86 (2010) no. 1, pp. 89-90. http://gdmltest.u-ga.fr/item/1272289544/