Rocky Mountain Journal of Mathematics

Lower bounds of the canonical height on quadratic twists of elliptic curves

Tadahisa Nara

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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.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 6 (2014), 2009-2027.

Dates
First available in Project Euclid: 2 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1422885105

Digital Object Identifier
doi:10.1216/RMJ-2014-44-6-2009

Mathematical Reviews number (MathSciNet)
MR3310959

Zentralblatt MATH identifier
1322.11059

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52] 11G50: Heights [See also 14G40, 37P30]
Secondary: 11G07: Elliptic curves over local fields [See also 14G20, 14H52]

Keywords
Elliptic curve Mordell-Weil group canonical height quadratic twist

Citation

Nara, Tadahisa. Lower bounds of the canonical height on quadratic twists of elliptic curves. Rocky Mountain J. Math. 44 (2014), no. 6, 2009--2027. doi:10.1216/RMJ-2014-44-6-2009. https://projecteuclid.org/euclid.rmjm/1422885105


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