Torsion of elliptic curves with rational 𝑗-invariant defined over number fields of prime degree

DOI10.1090/proc/15500zbMath1475.11113arXiv1912.04037OpenAlexW3133412345MaRDI QIDQ4992912

Tomislav Gužvić

Publication date: 10 June 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.04037

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52)

Related Items

Torsion for CM elliptic curves defined over number fields of degree 2𝑝, -adic images of Galois for elliptic curves over (and an appendix with John Voight), Torsion groups of elliptic curves over ℚ(μp∞), Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant, \(\mathbb{Q}\)-curves over odd degree number fields

Uses Software

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

Cites Work

• Unnamed Item
• Unnamed Item
• On the field of definition of \(p\)-torsion points on elliptic curves over the rationals
• The number of twists with large torsion of an elliptic curve
• Complete classification of the torsion structures of rational elliptic curves over quintic number fields
• Torsion of rational elliptic curves over cubic fields and sporadic points on \(X_1(n)\)
• Torsion groups of elliptic curves with integral j-invariant over pure cubic fields
• Torsion of rational elliptic curves over quartic Galois number fields
• Points of finite order on elliptic curves with complex multiplication
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Modular curves and the Eisenstein ideal
• The Magma algebra system. I: The user language
• On the minimal degree of definition of \(p\)-primary torsion subgroups of elliptic curves
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Bounds for the torsion of elliptic curves over number fields
• Elliptic curves over \(\mathbb {Q}\) and 2-adic images of Galois
• Torsion growth of rational elliptic curves in sextic number fields
• Cartan images and \(\ell \)-torsion points of elliptic curves with rational \(j\)-invariant
• Computation on elliptic curves with complex multiplication
• Torsion Groups of Elliptic Curves with Integral j-Invariant over General Cubic Number Fields
• THE GENERAL LINEAR GROUP OVER A RING
• COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
• Torsion points on elliptic curves defined over quadratic fields
• On the Modular Curves X ₀ (125), X ₁ (25), X ₁ (49)
• The Modular Curve X ₀ (169) and Rational Isogeny
• The modular curves X₀(65) and X₀(91) and rational isogeny
• The modular curve X₀(39) and rational isogeny
• Torsion subgroups of rational elliptic curves over the compositum of all cubic fields
• Torsion Subgroups of CM Elliptic Curves over Odd Degree Number Fields:
• Growth of torsion groups of elliptic curves upon base change
• On the torsion of rational elliptic curves over sextic fields
• Composite images of Galois for elliptic curves over $\mathbf {Q}$ and entanglement fields
• ON THE TORSION OF ELLIPTIC CURVES OVER QUARTIC NUMBER FIELDS