A $p$-adic algorithm to compute the Hilbert class polynomial

DOI10.1090/S0025-5718-08-02091-7zbMath1223.11073OpenAlexW2110949086MaRDI QIDQ3055076

Reinier Bröker

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-08-02091-7

Mathematics Subject Classification ID

Complex multiplication and moduli of abelian varieties (11G15) Other algebras and orders, and their zeta and (L)-functions (11R54) Analytic computations (11Y35)

Related Items (12)

Gross-Zagier type CM value formulas on \(X_0^\ast(p)\) ⋮ On the hardness of the computational ring-LWR problem and its applications ⋮ Computing the endomorphism ring of an ordinary elliptic curve over a finite field ⋮ CSIDH: an efficient post-quantum commutative group action ⋮ Computing Hilbert Class Polynomials ⋮ Modular polynomials via isogeny volcanoes ⋮ FINDING SINGULAR MODULI ON A COMPLEX LINE ⋮ A nonsplit sum of coefficients of modular forms ⋮ Accelerating the CM method ⋮ Choosing the correct elliptic curve in the CM method ⋮ Computing Hilbert class polynomials with the Chinese remainder theorem ⋮ Computing Class Polynomials for Abelian Surfaces

Cites Work

• Factoring integers with elliptic curves
• Nonsingular plane cubic curves over finite fields
• Counting points on elliptic curves over finite fields
• The complexity of class polynomial computation via floating point approximations
• A Rigorous Time Bound for Factoring Integers
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Algorithmic Number Theory
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