## Computing heights on elliptic curves

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- by Joseph H. Silverman PDF
- Math. Comp.
**51**(1988), 339-358 Request permission

## 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.

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## Additional Information

- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp.
**51**(1988), 339-358 - MSC: Primary 11G05; Secondary 11D25, 11Y40, 14G25, 14K15
- DOI: https://doi.org/10.1090/S0025-5718-1988-0942161-4
- MathSciNet review: 942161