Archimedean local height differences on elliptic curves

DOI10.4064/aa180714-7-12zbMath1453.11087arXiv1807.04153OpenAlexW2878880349WikidataQ127564189 ScholiaQ127564189MaRDI QIDQ5237103

Jan Steffen Müller, Corinna Stumpe

Publication date: 16 October 2019

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.04153

zbMATH Keywords

elliptic curvesrational pointsnumber fieldscanonical heightsheight constantArchimedean local heights

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Heights (11G50) Elliptic curves over local fields (11G07)

Uses Software

• Magma

Cites Work

• Height difference bounds for elliptic curves over number fields
• The Magma algebra system. I: The user language
• Infinite descent on elliptic curves
• The difference between the ordinary height and the canonical height on elliptic curves
• Canonical heights on genus-2 Jacobians
• Bornes optimales pour la différence entre la hauteur de Weil et la hauteur de Néron–Tate sur les courbes elliptiques sur Q
• Computing canonical heights on elliptic curves in quasi-linear time
• The Difference Between the Weil Height and the Canonical Height on Elliptic Curves
• An Explicit Theory of Heights for Hyperelliptic Jacobians of Genus Three
• On the height constant for curves of genus two
• Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

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