On Congruent Numbers with Three Prime Factors

On Congruent Numbers with Three Prime Factors

A method is given for constructing congruent numbers with three prime factors of the form 8 + 3. A family of such numbers is given for which the Mordell–Weil rank of their associated elliptic curves equals 2, the maximal rank and expected rank for a congruent number curve of this type.

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Veröffentlicht in:Integers (Berlin, Germany) Germany), 2011-10, Vol.11 (5), p.589-595
Hauptverfasser: Reinholz, Lindsey, Spearman, Blair K., Yang, Qiduan
Format: Artikel
Sprache:eng
Schlagworte:
Congruent Numbers
Elliptic Curve
Rank
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Zusammenfassung:A method is given for constructing congruent numbers with three prime factors of the form 8 + 3. A family of such numbers is given for which the Mordell–Weil rank of their associated elliptic curves equals 2, the maximal rank and expected rank for a congruent number curve of this type.
ISSN:1867-0652
DOI:10.1515/integ.2011.043