A bound for the conductor of an open subgroup of \(\mathrm{GL}_2\) associated to an elliptic curve

DOI10.2140/pjm.2020.308.307zbMath1465.11144arXiv1904.10431OpenAlexW3110971129MaRDI QIDQ827441

Nathan Jones

Publication date: 8 January 2021

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.10431

zbMATH Keywords

elliptic curvesGalois representations

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Galois representations (11F80)

Related Items (3)

A bound for the image conductor of a principally polarized abelian variety with open Galois image ⋮ Constants in Titchmarsh divisor problems for elliptic curves ⋮ Degree bounds for projective division fields associated to elliptic modules with a trivial endomorphism ring

Cites Work

• Unnamed Item
• On the field of definition of \(p\)-torsion points on elliptic curves over the rationals
• Rational points on \(X_0^+(p^r)\)
• Serre's uniformity problem in the split Cartan case
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Bounds for the torsion of elliptic curves over number fields
• Surjectivity of mod \(2^n\) representations of elliptic curves
• Constants in Titchmarsh divisor problems for elliptic curves
• On the level of modular curves that give rise to isolated \(j\)-invariants
• An infinite family of Serre curves
• Modular curves of prime-power level with infinitely many rational points
• Galois properties of points of finite order of elliptic curves
• Elliptic curves with 2-torsion contained in the 3-torsion field
• Elliptic curves with maximal Galois action on their torsion points
• A bound for the torsion conductor of a non-CM elliptic curve
• Galois Action on Division Points of Abelian Varieties with Real Multiplications
• On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves
• Composite images of Galois for elliptic curves over $\mathbf {Q}$ and entanglement fields
• Elliptic Curves and Wild Ramification
• Endliche Gruppen I

This page was built for publication: A bound for the conductor of an open subgroup of \(\mathrm{GL}_2\) associated to an elliptic curve