Supersingular j-invariants and the class number of ℚ(−p)

DOI10.1142/S1793042122500555zbMath1499.11227arXiv2101.04937OpenAlexW3211589583WikidataQ114071861 ScholiaQ114071861MaRDI QIDQ5864319

Lixia Luo, Guanju Xiao, Yingpu Deng

Publication date: 7 June 2022

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

Full work available at URL: https://arxiv.org/abs/2101.04937

zbMATH Keywords

class numberclass polynomialsimaginary quadratic ordersupersingular \(j\)-invariants

Mathematics Subject Classification ID

Quadratic extensions (11R11) Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Class numbers, class groups, discriminants (11R29)

Cites Work

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• The development of the number field sieve
• Supersingular j-invariants as singular moduli mod p
• Binary quadratic forms. An algorithmic approach
• Factoring integers with elliptic curves
• Computing Hilbert class polynomials with the Chinese remainder theorem
• Computation of class numbers of quadratic number fields
• A babystep-giantstep method for faster deterministic integer factorization
• On Singular Moduli for Arbitrary Discriminants
• The Arithmetic of Elliptic Curves
• On maximal orders of division quaternion algebras over the rational number field with certain optimal embeddings
• An exponent one-fifth algorithm for deterministic integer factorisation
• Character sums and deterministic polynomial root finding in finite fields
• Computing isogenies between supersingular elliptic curves over \(\mathbb {F}_p\)