Tag
Class Number
7 resources tagged “Class Number” across the knowledge library.
7 items
Article7 Aug 2026Complex Multiplication and Class NumbersThe link between curves with complex multiplication and class groups of imaginary quadratic orders, and the Hilbert class polynomial.2 min readRead MoreArticle7 Aug 2026Cyclic and Pure Cubic Field FamiliesCyclic cubic and pure cubic fields as parametrised families, with closed-form invariants that avoid general algorithms.2 min readRead MoreArticle7 Aug 2026Imaginary Quadratic Class Numbers by Counting Reduced FormsComputing class numbers and group structure for imaginary quadratic fields by enumerating reduced forms, and where the method runs out.2 min readRead MoreArticle7 Aug 2026Reduction of Positive Definite Binary FormsReducing a positive definite binary quadratic form to the unique reduced form in its class, and the resulting class number algorithm.2 min readRead MoreArticle7 Aug 2026The Ideal Class GroupThe class group as the obstruction to unique factorisation, its finiteness, and what a complete computation must produce.2 min readRead MoreGuide6 Aug 2026Class Groups, Units and the RegulatorThe ideal class group, Dirichlet's unit theorem, the regulator, Minkowski's bound, and the analytic class number formula used to verify computed values.4 min readRead MoreGuide6 Aug 2026Class Numbers of Imaginary Quadratic FieldsComputing class numbers of imaginary quadratic fields by enumeration of reduced forms, by analytic class number formulas, and by modular form methods, with the Gauss class number problem.4 min readRead More