Typically bounding torsion on elliptic curves with rational\n j-invariant

2021/02/20 by Tyler Genao, Genao, Tyler
Computer Science · Mathematics · #11G05 #11G15 #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2102.10417

openalex publication_date 2021/02/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

A family \F of elliptic curves defined over number fields is said\nto be typically bounded in torsion if the torsion subgroups E(F)[tors] of\nthose elliptic curves E_/F\∈ \F can be made uniformly bounded\nafter removing from \F those whose number field degrees lie in a\nsubset of \ℤ⁺ with arbitrarily small upper density. For every number\nfield F, we prove unconditionally that the family \E_F of elliptic\ncurves defined over number fields and with F-rational j-invariant is\ntypically bounded in torsion. For any integer d\∈\ℤ⁺, we also\nstrengthen a result on typically bounding torsion for the family\n\E_d of elliptic curves defined over number fields and with degree\nd j-invariant.\n

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