Abstract
The Hasse-Minkowski theorem implies that the existence of rational points on a curve of genus 0 can be decided by local arguments, and then the rational points have a parametrization in terms of rational functions of a single parameter t ∈ ℙ1(ℚ), or equivalently a pair of coprime integers (see for example Corollary 6.3.6).
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© 2007 Springer Science + Business Media, LLC
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(2007). Diophantine Aspects of Elliptic Curves. In: Number Theory. Graduate Texts in Mathematics, vol 239. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49923-9_8
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DOI: https://doi.org/10.1007/978-0-387-49923-9_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-49922-2
Online ISBN: 978-0-387-49923-9
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