Bielliptic modular curves

DOI10.1006/jnth.1998.2343zbMath0964.11029OpenAlexW1984754959MaRDI QIDQ1293694

Francesc Bars Cortina

Publication date: 24 June 2001

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

Full work available at URL: https://doi.org/10.1006/jnth.1998.2343

zbMATH Keywords

modular curvesquadratic pointsbielliptic and hyperelliptic curves

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) [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)] Algebraic theory of abelian varieties (14K05)

Related Items (21)

Quadratic points on bielliptic modular curves ⋮ Weierstrass points on modular curves X₀(N) fixed by the Atkin–Lehner involutions ⋮ Bielliptic quotient modular curves of 𝑋₀(𝑁) ⋮ Hyperelliptic modular curves and isogenies of elliptic curves over quadratic fields ⋮ Bielliptic modular curves \(X_0^+(N)\) ⋮ Modular curves with infinitely many quartic points ⋮ The least degree of a CM point on a modular curve ⋮ Gonality of the modular curve 𝑋₀(𝑁) ⋮ AN "ANTI-HASSE PRINCIPLE" FOR PRIME TWISTS ⋮ On the Drinfeld modular curves \(X_ 1(\mathfrak n)\). ⋮ Modular curves with infinitely many cubic points ⋮ Quadratic points on modular curves with infinite Mordell–Weil group ⋮ Quadratic points on modular curves ⋮ A moduli approach to quadratic \(\mathbb{Q}\)-curves realizing projective mod \(p\) Galois representations ⋮ On quadratic points of classical modular curves ⋮ Bielliptic modular curves $X_0^*(N)$ with square-free levels ⋮ Bielliptic intermediate modular curves ⋮ Rational points on twisted modular curves ⋮ Bielliptic quotient modular curves with \(N\) square-free ⋮ Generalized class polynomials ⋮ Bielliptic modular curves \(X_1(M,N)\)

Uses Software

• ecdata

Cites Work

• Arithmetic of Weil curves
• Hecke operators on \(\Gamma_0(m)\)
• Bielliptic Curves and Symmetric Products
• Hyperelliptic modular curves
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