Archimedean local height differences on elliptic curves

2018/07/11 by J. Steffen Müller, Müller, J. Steffen, Corinna Stumpe +1
Computer Science · Mathematics · #11G05 #11G07 (secondary #11G50 (primary) 14G05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1807.04153

openalex publication_date 2018/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To compute generators for the Mordell-Weil group of an elliptic curve over a number field, one needs to bound the difference between the naive and the canonical height from above. We give an elementary and fast method to compute an upper bound for the local contribution to this difference at an archimedean place, which sometimes gives better results than previous algorithms.

Citations

• Solving S-unit, Mordell, Thue, Thue-Mahler and generalized\n Ramanujan-Nagell equations via Shimura-Taniyama conjecture

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