On the computation of quadratic 2-class groups

DOI10.5802/jtnb.170zbMath0870.11080OpenAlexW2334411759MaRDI QIDQ679092

Peter Stevenhagen, Wieb Bosma

Publication date: 11 September 1997

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1996__8_2_283_0

zbMATH Keywords

computationternary quadratic forms2-class groupambiguous binary forms

Mathematics Subject Classification ID

Quadratic extensions (11R11) General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) General binary quadratic forms (11E16)

Related Items

Dirichlet’s proof of the three-square theorem: An algorithmic perspective, Orientations and the supersingular endomorphism ring problem, Breaking the decisional Diffie-Hellman problem for class group actions using genus theory: extended version, Structure of 2-class groups in the \(\mathbb{Z}_2\)-extensions of certain real quadratic fields, \textsf{Dew}: a transparent constant-sized polynomial commitment scheme, Inner product functional commitments with constant-size public parameters and openings, On the parametrization of solutions of quadratic equations, Congruences for odd class numbers of quadratic fields with odd discriminant, Genus character L‐functions of quadratic orders and class numbers, On efficient computation of the 2-parts of ideal class groups of quadratic fields, Selected Applications of LLL in Number Theory, Congruences relating class numbers of quadratic orders and Zagier's sums, Transparent SNARKs from DARK compilers, Breaking the decisional Diffie-Hellman problem for class group actions using genus theory, On the decisional Diffie-Hellman problem for class group actions on oriented elliptic curves, Rational isogenies from irrational endomorphisms

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Magma algebra system. I: The user language
• A Rigorous Subexponential Algorithm For Computation of Class Groups
• On the Computational Complexity of Determining the Solvability or Unsolvability of the Equation X 2 - DY 2 = -1
• Worst-case complexity bounds for algorithms in the theory of integral quadratic forms
• Corrigenda
• The Number of Real Quadratic Fields Having Units of Negative Norm
• Density computations for real quadratic units