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

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

2011-10-31

arxiv.org/abs/1110.6710v1

Mathematics

Number Theory

Scientific paper

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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