Composite images of Galois for elliptic curves over $\mathbf {Q}$ and entanglement fields

DOI10.1090/mcom/3426zbMath1470.11154arXiv1707.04646OpenAlexW2962692779MaRDI QIDQ5380098

Jackson S. Morrow

Publication date: 14 June 2019

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

Full work available at URL: https://arxiv.org/abs/1707.04646

zbMATH Keywords

elliptic curvesrational pointsentanglement fields

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Counting solutions of Diophantine equations (11D45) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18)

Related Items

A bound for the conductor of an open subgroup of \(\mathrm{GL}_2\) associated to an elliptic curve, A group theoretic perspective on entanglements of division fields, Serre’s Constant of Elliptic Curves Over the Rationals, Coincidences of division fields, -adic images of Galois for elliptic curves over (and an appendix with John Voight), Towards a classification of entanglements of Galois representations attached to elliptic curves, Torsion growth of rational elliptic curves in sextic number fields, Elliptic curves with non-abelian entanglements, Torsion of elliptic curves with rational 𝑗-invariant defined over number fields of prime degree, Some uniform bounds for elliptic curves over \(\mathbb{Q} \), On the level of modular curves that give rise to isolated \(j\)-invariants

Uses Software

• Magma
• LMFDB
• GitHub
• ell-adic-galois-images

Cites Work

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