Equations for the modular curve 𝑋₁(𝑁) and models of elliptic curves with torsion points

DOI10.1090/S0025-5718-10-02332-XzbMath1252.11038MaRDI QIDQ3160745

Houria Baaziz

Publication date: 8 October 2010

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

zbMATH Keywords

elliptic curvesmodular curvestorsion points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Modular and automorphic functions (11F03) Arithmetic aspects of modular and Shimura varieties (11G18) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items

Trielliptic modular curves $X_1(N)$ ⋮ EXCEPTIONAL ELLIPTIC CURVES OVER QUARTIC FIELDS ⋮ Construction of anti-cyclotomic Euler systems of modular abelian varieties, and the ranks of their Mordell-Weil groups ⋮ On smooth plane models for modular curves of Shimura type ⋮ Torsion of elliptic curves over cubic fields ⋮ Families of elliptic curves with prescribed torsion subgroups over dihedral quartic fields ⋮ Constructing elliptic curves over finite fields with prescribed torsion ⋮ Torsion of elliptic curves over imaginary quadratic fields of class number 1 ⋮ On the computation of coefficients of modular forms: The reduction modulo $p$ approach ⋮ A divisor formula and a bound on the \(\mathbb{Q} \)-gonality of the modular curve \(X_1(N)\) ⋮ Families of elliptic curves over cyclic cubic number fields with prescribed torsion ⋮ Automorphism groups of hyperelliptic modular curves ⋮ Minimal models of rational elliptic curves with non-trivial torsion ⋮ Torsion of elliptic curves over real quadratic fields of smallest discriminant ⋮ DEFINING EQUATIONS OF X₁(2N)

Cites Work

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• Unités d'une famille de corps cycliques réels de degré 6 liés à la courbe modulaire \(X_ 1(13)\). (Units of a family of real cyclic fields of degree 6 related to the modular curve \(X_ 1(13))\)
• Defining equations of modular curves
• Generators and defining equation of the modular function field of the group Γ₁(N)
• Note on a Polynomial of Emma Lehmer
• Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields
• A Family of Cyclic Quartic Fields Arising from Modular Curves