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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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