
Open access
Date
2019Type
- Journal Article
ETH Bibliography
yes
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Abstract
We investigate the geometry of Hessian curves H_c : x^3 + y^3 + z^3 + cxyz = 0. In particular, we present an elementary characterisation of Hessian curves with torsion group Z/6Z. As an application we show, for example, that a result of Mordell’s implies that the equation 7m^4 −26m^2e^2 − 49e^4 − n^2 = 0 does not have a solution in positive integers. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000314721Publication status
publishedExternal links
Journal / series
International Electronic Journal of Pure and Applied MathematicsVolume
Pages / Article No.
Publisher
Academic PublicationsSubject
Hessian curves; diophantine equations; elliptic curvesOrganisational unit
03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
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ETH Bibliography
yes
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