Abstract
Let C be a non-singular cubic curve given by an equation
with integer coefficients. We have seen that if C has a rational point (possibly at infinity), then the set of all rational points on C forms a finitely generated abelian group. So we can get every rational point on C by starting from some finite set and adding points using the geometrically defined group law.
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© 1992 Springer Science+Business Media New York
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Silverman, J.H., Tate, J. (1992). Integer Points on Cubic Curves. In: Rational Points on Elliptic Curves. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4252-7_6
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DOI: https://doi.org/10.1007/978-1-4757-4252-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3101-6
Online ISBN: 978-1-4757-4252-7
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