Computing heights on elliptic curves

Silverman, Joseph H.

doi:10.1090/S0025-5718-1988-0942161-4

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
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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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