LOWER BOUNDS OF THE CANONICAL HEIGHT ON QUADRATIC TWISTS OF ELLIPTIC CURVES

摘要

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.