Torsion growth of rational elliptic curves in sextic number fields

DOI10.1016/j.jnt.2020.09.010zbMath1469.14071arXiv1910.01561OpenAlexW3093901597MaRDI QIDQ2212673

Tomislav Gužvić

Publication date: 24 November 2020

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.01561

zbMATH Keywords

elliptic curvestorsion group

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Other number fields (11R21) Elliptic curves (14H52) Galois representations (11F80)

Related Items (5)

Torsion groups of elliptic curves over ℚ(μp∞) ⋮ Torsion growth over number fields of degree \(pq\) ⋮ Growth of torsion groups of elliptic curves over number fields without rationally defined CM ⋮ Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields ⋮ Torsion of elliptic curves with rational 𝑗-invariant defined over number fields of prime degree

Uses Software

• Magma
• ell-adic-galois-images

Cites Work

• Unnamed Item
• Unnamed Item
• Torsion of rational elliptic curves over cubic fields
• 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 of rational elliptic curves over quartic Galois number fields
• Complete classification of torsion of elliptic curves over quadratic cyclotomic 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
• Modular curves of prime-power level with infinitely many rational points
• Elliptic divisibility sequences over certain curves
• Elliptic curves with 2-torsion contained in the 3-torsion field
• Computation on elliptic curves with complex multiplication
• 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:
• On the torsion of elliptic curves over cubic number fields
• Growth of torsion groups of elliptic curves upon base change
• On the torsion of rational elliptic curves over sextic fields
• Torsion subgroups of elliptic curves over quintic and sextic number fields
• Composite images of Galois for elliptic curves over $\mathbf {Q}$ and entanglement fields
• ON THE TORSION OF ELLIPTIC CURVES OVER QUARTIC NUMBER FIELDS

This page was built for publication: Torsion growth of rational elliptic curves in sextic number fields