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Computing all S-integral points on elliptic curves

Published online by Cambridge University Press:  01 November 1999

ATTILA PETHŐ ,
HORST G. ZIMMER ,
JOSEF GEBEL  and
EMANUEL HERRMANN
ATTILA PETHŐ
Affiliation:
Institut of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, P.O. Box 12, Hungary
HORST G. ZIMMER
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
JOSEF GEBEL
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
EMANUEL HERRMANN
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
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Abstract

Let the elliptic curve E be defined by the equation

formula here

with a1, …, a6 ∈ ℤ. Define a finite set of places S = {q1, …, qs−1, qs = ∞} of ℚ and put Q = max {q1, …, qs−1}. Let E(ℚ) denote the set of (x, y) ∈ ℚ2 satisfying (1) and the infinite point [Oscr ].

The multiplicative height of a rational point P = (x, y) ∈ E(ℚ) is defined as the following product over all places q of ℚ (including q = ∞):

formula here

where the [mid ]x[mid ]qs are the normalized multiplicative absolute values of ℚ corresponding to the places q.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 3 , November 1999 , pp. 383 - 402
Copyright
© The Cambridge Philosophical Society 1999

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