High Quality Content by WIKIPEDIA articles! n number theory, the Neron–Tate height (or canonical height) is a quadratic form on the Mordell-Weil group of rational points of an abelian variety defined over a global field. It is named after Andre Neron and John Tate.On an elliptic curve, the Neron-Severi group is of rank one and has a unique ample generator, so this generator is often used to define the Neron–Tate height, which is denoted h without reference to a particular line bundle. (However, the height that naturally appears in the statement of the Birch–Swinnerton-Dyer conjecture is twice this height.) On abelian varieties of higher dimension, there need not be a particular choice of smallest ample line bundle to be used in defining the Neron–Tate height.

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