Bull. Austral. Math. Soc. 72(2) pp.177--186, 2005.
Height estimates on cubic twists of the Fermat elliptic curve
Tomasz Jedrzejak |
.
Abstract
We give bounds for the canonical height of rational and integral points on cubic twists of the Fermat elliptic curve. As a corollary we prove that there is no integral arithmetic progression on certain curves in this family.
Click to download PDF of this article (free access until July 2006)
| (Metadata: XML, RSS, BibTeX) | MathSciNet: MR2183401 |
References
- M.A. Bennet
On the representation of unity by binary cubic forms
(preprint). - A. Bremner, J.H. Silverman and N. Tzanakis
Integral points in arithmetic progression on y 2=x( x 2-n 2)
J. Number Theory , 80 ; 2000, pp. 187--208. - J.E. Cremona, http://www.maths.nott.ac.uk/personal/jec/ftp/progs.
- M. Hindry and J.H. Silverman
The cannonical heights and integral points on elliptic curves
Invent. Math. , 93 ; 1998, pp. 419--450. - S. Lang
Elliptic curves: Diophantine analysis
Springer-Verlag ; 1978, Grundlehren der Math. Wiss , Berlin, New York . - J.H. Silverman
Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Math. , 151
Springer-Verlag , New York ; 1994. - J. Tate
Algorithm for determining the type of a singular fiber in an elliptic pencil,
in Modular Functions of One Variable IV, Lecture Notes in Math. 476
Springer-Verlag , Berlin, Heidelberg, New York ; 1975.
ISSN 0004-9727