Computing Heights on Elliptic Curves
- 1 July 1988
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 51 (183) , 339-358
- https://doi.org/10.2307/2008597
Abstract
We describe how to compute the canonical height of points on elliptic curves. Tate has given a rapidly converging series for Archimedean local heights over R. We describe a modified version of Tate’s series which also converges over C, and give an efficient procedure for calculating local heights at non-Archimedean places. In this way we can calculate heights over number fields having complex embeddings. We also give explicit estimates for the tail of our series, and present several examples.Keywords
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