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Computing all S-integral points on elliptic curves
Published online by Cambridge University Press: 01 November 1999
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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