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arXiv · 1110.6710

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

T. Nara
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Abstract

We compute a lower bound of the canonical height on quadratic twists of certain elliptic curves. Also we show a simple method for constructing families of quadratic twists with an explicit rational point. % from cubic polynomials. 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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T. Nara. 2011-10-31. Lower bounds of the canonical height on quadratic twists of elliptic curves. https://arxiv.org/abs/1110.6710

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