Trielliptic modular curves $X_1(N)$

DOI10.4064/aa220527-7-10OpenAlexW4312790167MaRDI QIDQ5058638

Daeyeol Jeon

Publication date: 21 December 2022

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa220527-7-10

zbMATH Keywords

trielliptic mapstrielliptic modular curves

Mathematics Subject Classification ID

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)]

Uses Software

• ecdata

Cites Work

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• Gonality of the modular curve \(X_1(N)\)
• Torsion of rational elliptic curves over cubic fields and sporadic points on \(X_1(n)\)
• Stickelberger elements and modular parametrizations of elliptic curves
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• Modular curves and the Eisenstein ideal
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• Sporadic cubic torsion
• Bielliptic intermediate modular curves
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• Equations for the modular curve 𝑋₁(𝑁) and models of elliptic curves with torsion points
• Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields
• Torsion points on elliptic curves defined over quadratic fields
• Elliptic Curves
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Bielliptic modular curves X₁(N)
• On the torsion of elliptic curves over cubic number fields
• Constructing elliptic curves over finite fields with prescribed torsion