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2014 Lower bounds of the canonical height on quadratic twists of elliptic curves
Tadahisa Nara
Rocky Mountain J. Math. 44(6): 2009-2027 (2014). DOI: 10.1216/RMJ-2014-44-6-2009

Abstract

We compute a lower bound of the canonical height on quadratic twists of elliptic curves over $\Q$. Also, we show a simple method for constructing families of quadratic twists with an explicit rational point. Using the above lower bound, we show that the explicit rational point is primitive as an element of the Mordell-Weil group.

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Tadahisa Nara. "Lower bounds of the canonical height on quadratic twists of elliptic curves." Rocky Mountain J. Math. 44 (6) 2009 - 2027, 2014. https://doi.org/10.1216/RMJ-2014-44-6-2009

Information

Published: 2014
First available in Project Euclid: 2 February 2015

zbMATH: 1322.11059
MathSciNet: MR3310959
Digital Object Identifier: 10.1216/RMJ-2014-44-6-2009

Subjects:
Primary: 11G05, 11G50
Secondary: 11G07

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.44 • No. 6 • 2014
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