Torsion points on elliptic curves over number fields of small degree

DOI10.2140/ant.2023.17.267OpenAlexW4360838536MaRDI QIDQ2691610

Maarten Derickx, William A. Stein, Sheldon Kamienny, Michael Stoll

Publication date: 29 March 2023

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.00364

zbMATH Keywords

torsion subgroupelliptic curvetorsion pointnumber fields of small degree

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Elliptic curves (14H52) Global ground fields in algebraic geometry (14G25)

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Quadratic points on bielliptic modular curves, A criterion to rule out torsion groups for elliptic curves over number fields, On the field of definition of \(p\)-torsion points on elliptic curves over the rationals, On elliptic curves with p-isogenies over quadratic fields, \(\mathbb{Q}\)-curves, Hecke characters, and some Diophantine equations. II, Cyclic isogenies of elliptic curves over fixed quadratic fields, Isogenies of non-CM elliptic curves with rational j-invariants over number fields, Computing quadratic points on modular curves 𝑋₀(𝑁), On the torsion of rational elliptic curves over quartic fields, Quadratic points on modular curves, A multi-Frey approach to Fermat equations of signature $(r,r,p)$, Torsion of rational elliptic curves over quadratic fields, Selmer groups of twists of elliptic curves over \(K\) with \(K\)-rational torsion points, On ternary Diophantine equations of signature(p,p,2)over number fields, Uniform boundedness in terms of ramification, On Fermat's equation over some quadratic imaginary number fields

Cites Work

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• Gonality of the modular curve \(X_1(N)\)
• No 17-torsion on elliptic curves over cubic number fields
• 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
• \(J_1(p)\) has connected fibers
• Torsion des courbes elliptiques sur les corps cubiques. (Torsion of elliptic curves over cubic fields)
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Two theorems on modular curves
• Bounds for the torsion of elliptic curves over number fields
• Families of elliptic curves over cubic number fields with prescribed torsion subgroups
• Families of elliptic curves over quartic number fields with prescribed torsion subgroups
• A linear lower bound on the gonality of modular curves
• Les Schémas de Modules de Courbes Elliptiques
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE)
• Constructing elliptic curves over finite fields with prescribed torsion
• Abelian varieties over finite fields