A family of congruent number elliptic curves of rank three
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Author / Producer
Date
2023
Publication Type
Journal Article
ETH Bibliography
yes
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Abstract
Recent progress in the theory of Heron triangles and their elliptic curves led to new families of congruent number elliptic curves with rank at least two. Based on these results, we derive a parametric family of congruent number elliptic curves with rank at least three. It turns out that this family is isomorphic to a family which was recently discovered by the third-named author, however the new approach is simpler, more flexible and gives new insight. In particular, it provides in addition three formulae for congruent numbers.
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Publication status
published
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Editor
Book title
Journal / series
Volume
46 (6)
Pages / Article No.
1131 - 1137
Publisher
Taylor & Francis
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Congruent number; elliptic curve; rank
Organisational unit
08848 - Halbeisen, Lorenz (Tit.-Prof.) / Halbeisen, Lorenz (Tit.-Prof.)
03874 - Hungerbühler, Norbert / Hungerbühler, Norbert