Congruent numbers over real number fields

Volume 128 / 2012

Tomasz Jędrzejak Colloquium Mathematicum 128 (2012), 179-186 MSC: Primary 11G05; Secondary 14H52. DOI: 10.4064/cm128-2-3


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.


  • Tomasz JędrzejakInstitute of Mathematics
    University of Szczecin
    Wielkopolska 15
    70-451 Szczecin, Poland

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image