A divisor formula and a bound on the \(\mathbb{Q} \)-gonality of the modular curve \(X_1(N)\)

DOI10.1007/s40993-021-00243-3OpenAlexW3137960833MaRDI QIDQ2020004

Mark van Hoeij, Hanson Smith

Publication date: 23 April 2021

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

Full work available at URL: https://arxiv.org/abs/2004.13644

zbMATH Keywords

modular curvesgonalitymodular unitsSiegel functionstorsion points on elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Modular and automorphic functions (11F03) Elliptic curves (14H52) Modular and Shimura varieties (14G35) Elliptic and modular units (11G16)

Related Items

Ramification in division fields and sporadic points on modular curves, Sporadic cubic torsion

Uses Software

• DLMF

Cites Work

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• Gonality of the modular curve \(X_1(N)\)
• Cuspidal \(\mathbb Q\)-rational torsion subgroup of \(J(\Gamma)\) of level \(p\)
• Modular units and cuspidal divisor class groups of \(X_1(N)\)
• Torsion of rational elliptic curves over cubic fields and sporadic points on \(X_1(n)\)
• A cuspidal class number formula for the modular curves \(X_1(N)\)
• Cuspidal class number formula for the modular curves \(X_ 1(p)\)
• On the level of modular curves that give rise to isolated \(j\)-invariants
• Modular curves of prime-power level with infinitely many rational points
• Equations for the modular curve 𝑋₁(𝑁) and models of elliptic curves with torsion points
• Structure of the cuspidal rational torsion subgroup of J ₁ (p ⁿ )
• The Arithmetic of Elliptic Curves
• Cuspidal divisor class groups of non-split Cartan modular curves
• Constructing elliptic curves over finite fields with prescribed torsion
• The kernel of the Eisenstein ideal