Sporadic cubic torsion

DOI10.2140/ant.2021.15.1837zbMath1479.14039arXiv2007.13929OpenAlexW3209836273WikidataQ114045557 ScholiaQ114045557MaRDI QIDQ2239246

Anastassia Etropolski, Jackson S. Morrow, David Zureick-Brown, Maarten Derickx, Mark van Hoeij

Publication date: 3 November 2021

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

Full work available at URL: https://arxiv.org/abs/2007.13929

zbMATH Keywords

elliptic curvesmodular curvesfinitely many cubic points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50) Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Computational aspects of algebraic curves (14Q05) Arithmetic aspects of modular and Shimura varieties (11G18)

Related Items (19)

Quadratic points on bielliptic modular curves ⋮ Trielliptic modular curves $X_1(N)$ ⋮ Torsion for CM elliptic curves defined over number fields of degree 2𝑝 ⋮ Typically bounding torsion on elliptic curves with rational \(j\)-invariant ⋮ On the problem of periodicity of continued fraction expansions of for cubic polynomials over algebraic number fields ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Ramification in division fields and sporadic points on modular curves ⋮ Torsion groups of elliptic curves over ℚ(μp∞) ⋮ Torsion growth over number fields of degree \(pq\) ⋮ Cyclic isogenies of elliptic curves over fixed quadratic fields ⋮ RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS ⋮ The least degree of a CM point on a modular curve ⋮ Gonality of the modular curve 𝑋₀(𝑁) ⋮ Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant ⋮ Computing quadratic points on modular curves 𝑋₀(𝑁) ⋮ Determination of the modular Jacobian varieties \(J_1(M,MN)\) with the Mordell-Weil rank zero ⋮ Elliptic curves with a point of order \(13\) defined over cyclic cubic fields ⋮ On the level of modular curves that give rise to isolated \(j\)-invariants ⋮ Torsion of elliptic curves in the compositum of Dihedral fields

Uses Software

• Maple

Cites Work

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• On the field of definition of \(p\)-torsion points on elliptic curves over the rationals
• Eisenstein ideals and the rational torsion subgroups of modular Jacobian varieties
• Gonality of the modular curve \(X_1(N)\)
• The \(\mathbb{Q}\)-rational cuspidal group of \(J_{1}(2p)\)
• No 17-torsion on elliptic curves over cubic number fields
• Cuspidal \(\mathbb Q\)-rational torsion subgroup of \(J(\Gamma)\) of level \(p\)
• Cuspidal class number of the tower of modular curves \(X_1(Np^n)\)
• Modular units and cuspidal divisor class groups of \(X_1(N)\)
• Torsion of rational elliptic curves over cubic fields and sporadic points on \(X_1(n)\)
• The cuspidal class number formula for the modular curves \(X_1(2p)\)
• The cuspidal class number formula for the modular curves \(X_1(2^{2n+1})\)
• A cuspidal class number formula for the modular curves \(X_1(N)\)
• Galois properties of torsion points on abelian varieties
• On the number of Q-isomorphism classes of elliptic curves in each Q- isogeny class
• Cuspidal class number formula for the modular curves \(X_ 1(p)\)
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Curves with infinitely many points of fixed degree
• The Magma algebra system. I: The user language
• Determinantal formula for the cuspidal class number of the modular curve \(X_1(m)\)
• \(J_1(p)\) has connected fibers
• Torsion des courbes elliptiques sur les corps cubiques. (Torsion of elliptic curves over cubic fields)
• On the cyclic torsion of elliptic curves over cubic number fields
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Bounds for the torsion of elliptic curves over number fields
• The cuspidal class number formula for the modular curves \(X_ 1(3^ m)\)
• Hanoi lectures on the arithmetic of hyperelliptic curves
• Elliptic curves over \(\mathbb {Q}\) and 2-adic images of Galois
• A divisor formula and a bound on the \(\mathbb{Q} \)-gonality of the modular curve \(X_1(N)\)
• On the cyclic torsion of elliptic curves over cubic number fields. II
• Families of elliptic curves over cubic number fields with prescribed torsion subgroups
• Structure of the cuspidal rational torsion subgroup of J ₁ (p ⁿ )
• p-Torsion points on elliptic curves defined over quadratic fields
• Torsion points on elliptic curves defined over quadratic fields
• Trigonal modular curves
• On the torsion of elliptic curves over cubic number fields
• Quadratic points on modular curves
• Constructing elliptic curves over finite fields with prescribed torsion
• The kernel of the Eisenstein ideal

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