On the level of modular curves that give rise to isolated \(j\)-invariants

DOI10.1016/j.aim.2019.106824zbMath1472.11190arXiv1808.04520OpenAlexW2980197538WikidataQ127119230 ScholiaQ127119230MaRDI QIDQ2335480

Yuan Liu, Bianca Viray, Frances Odumodu, Abbey Bourdon, Özlem Ejder

Publication date: 14 November 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.04520

zbMATH Keywords

modular curvesisolated pointsFaltings's theoremMerel's uniform boundedness theoremSerre's uniformity conjecturesporadic points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items (8)

Isolated points on \(X_1(\ell^n)\) with rational \(j\)-invariant ⋮ A bound for the conductor of an open subgroup of \(\mathrm{GL}_2\) associated to an elliptic curve ⋮ Typically bounding torsion on elliptic curves with rational \(j\)-invariant ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Ramification in division fields and sporadic points on modular curves ⋮ The least degree of a CM point on a modular curve ⋮ Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant ⋮ A divisor formula and a bound on the \(\mathbb{Q} \)-gonality of the modular curve \(X_1(N)\)

Uses Software

• ell-adic-galois-images

Cites Work

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