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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Computing heights on elliptic curves


Author: Joseph H. Silverman
Journal: Math. Comp. 51 (1988), 339-358
MSC: Primary 11G05; Secondary 11D25, 11Y40, 14G25, 14K15
MathSciNet review: 942161
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1988-0942161-4
PII: S 0025-5718(1988)0942161-4
Article copyright: © Copyright 1988 American Mathematical Society