Computing heights on elliptic curves

Author:
Joseph H. Silverman

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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Article copyright:
© Copyright 1988
American Mathematical Society