Computing canonical heights on elliptic curves in quasi-linear time

DOI10.1112/S1461157016000139zbMath1372.11068arXiv1509.08748OpenAlexW2196962921WikidataQ64387966 ScholiaQ64387966MaRDI QIDQ2971024

Jan Steffen Müller, Michael Stoll

Publication date: 4 April 2017

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.08748

zbMATH Keywords

heightelliptic curvesKummer coordinates

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Number-theoretic algorithms; complexity (11Y16) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items

Computing unit groups of curves ⋮ Explicit arithmetic intersection theory and computation of Néron-Tate heights ⋮ Archimedean local height differences on elliptic curves ⋮ Computing canonical heights on the projective line with no factorization

Uses Software

• Magma

Cites Work

• Height difference bounds for elliptic curves over number fields
• The Magma algebra system. I: The user language
• Approximating rings of integers in number fields
• Quasi-functions and heights on abelian varieties
• Computing canonical heights with little (or no) factorization
• Computation of the Neron-Tate Height on Elliptic Curves
• Factoring into coprimes in essentially linear time