The least degree of a CM point on a modular curve

DOI10.1112/jlms.12518OpenAlexW4211011644MaRDI QIDQ6176771

Paul Pollack, Tyler Genao, Pete L. Clark, Frederick Saia

Publication date: 24 August 2023

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/jlms.12518

Mathematics Subject Classification ID

Complex multiplication and moduli of abelian varieties (11G15) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (6)

Quadratic points on bielliptic modular curves ⋮ Torsion for CM elliptic curves defined over number fields of degree 2𝑝 ⋮ Ramification in division fields and sporadic points on modular curves ⋮ Cyclic isogenies of elliptic curves over fixed quadratic fields ⋮ Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant ⋮ Computing quadratic points on modular curves 𝑋₀(𝑁)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gonality of the modular curve \(X_1(N)\)
• Anatomy of torsion in the CM case
• Über die kleinste quadratfreie Zahl einer arithmetischen Reihe
• On the Hasse principle for Shimura curves
• Rational torsion in complex-multiplication elliptic curves
• Torsion bounds for elliptic curves and Drinfeld modules
• Divisibilite de certaines fonctions arithmétiques
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Bielliptic modular curves
• Curves with infinitely many points of fixed degree
• Typically bounding torsion
• Bounds for the torsion of elliptic curves over number fields
• Acyclotomy of torsion in the CM case
• Sporadic cubic torsion
• Torsion points and Galois representations on CM elliptic curves
• On the level of modular curves that give rise to isolated \(j\)-invariants
• Modular curves of prime-power level with infinitely many rational points
• The truth about torsion in the CM case
• Galois properties of points of finite order of elliptic curves
• Computation on elliptic curves with complex multiplication
• A linear lower bound on the gonality of modular curves
• The distribution of quadratic residues and non‐residues
• On the Modular Curves X ₀ (125), X ₁ (25), X ₁ (49)
• A character-sum estimate and applications
• Sur le nombre de points de torsion rationnels sur une courbe elliptique
• Class numbers of imaginary quadratic fields
• A Rate Estimate in Billingsleys Theorem for the Size Distribution of Large Prime Factors
• The truth about torsion in the CM case, II
• Torsion Subgroups of CM Elliptic Curves over Odd Degree Number Fields:
• Über die Classenzahl quadratischer Zahlkörper
• Les Schémas de Modules de Courbes Elliptiques
• 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
• TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE)
• Torsion points and isogenies on CM elliptic curves
• Conditional bounds for the least quadratic non-residue and related problems
• Torsion subgroups of elliptic curves over quintic and sextic number fields
• Torsion points on CM elliptic curves over real number fields
• ON THE TORSION OF ELLIPTIC CURVES OVER QUARTIC NUMBER FIELDS
• Values of arithmetical functions equal to a sum of two squares
• Über den kleinsten positiven quadratischen Nichtrest nach einer Primzahl
• Algorithmic Number Theory

This page was built for publication: The least degree of a CM point on a modular curve