Computing models for quotients of modular curves

DOI10.1007/s40993-021-00276-8zbMath1478.14046arXiv2101.03797OpenAlexW3189607597MaRDI QIDQ2045741

Josha Box

Publication date: 13 August 2021

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

Full work available at URL: https://arxiv.org/abs/2101.03797

zbMATH Keywords

algorithmsmodular curvesmodular forms

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items

Elliptic curves over totally real quartic fields not containing √5 are modular, On smooth plane models for modular curves of Shimura type

Uses Software

• GitHub
• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tetrahedral elliptic curves and the local-global principle for isogenies
• Normalizers of non-split Cartan subgroups, modular curves, and the class number one problem
• An exceptional isomorphism between modular curves of level 13
• Fourier expansions at cusps
• A variant of Petri's analysis of the canonical ideal of an algebraic curve
• Twists of newforms and pseudo-eigenvalues of \(W\)-operators
• Rational points on \(X^ +_ 0(N)\) and quadratic \(\mathbb Q\)-curves.
• Elliptic curves over totally real cubic fields are modular
• Elliptic curves over real quadratic fields are modular
• Hecke operators on \(\Gamma_0(m)\)
• Galois properties of points of finite order of elliptic curves
• Hyperelliptic modular curves and isogenies of elliptic curves over quadratic fields
• Elliptic curves with maximal Galois action on their torsion points
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• Monstrous Moonshine
• Modularity of certain potentially Barsotti-Tate Galois representations
• Les Schémas de Modules de Courbes Elliptiques