Congruent numbers over real number fields
Volume 128 / 2012
Colloquium Mathematicum 128 (2012), 179-186
MSC: Primary 11G05; Secondary 14H52.
DOI: 10.4064/cm128-2-3
Abstract
It is classical that a natural number $n$ is congruent iff the rank of $\mathbb{Q}$-points on $E_{n}:y^{2}=x^{3}-n^{2}x$ is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.
