Engineering↗
Complex Multiplication and Class Numbers
The link between curves with complex multiplication and class groups of imaginary quadratic orders, and the Hilbert class polynomial.
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Class Number
Every page in the KEVOS library tagged Class Number. 7 pages.
Engineering↗
Cyclic and Pure Cubic Field Families
Cyclic cubic and pure cubic fields as parametrised families, with closed-form invariants that avoid general algorithms.
Engineering↗
Imaginary Quadratic Class Numbers by Counting Reduced Forms
Computing class numbers and group structure for imaginary quadratic fields by enumerating reduced forms, and where the method runs out.
Engineering↗
Reduction of Positive Definite Binary Forms
Reducing a positive definite binary quadratic form to the unique reduced form in its class, and the resulting class number algorithm.
Engineering↗
The Ideal Class Group
The class group as the obstruction to unique factorisation, its finiteness, and what a complete computation must produce.
Engineering↗
Class Groups, Units and the Regulator
The ideal class group, Dirichlet's unit theorem, the regulator, Minkowski's bound, and the analytic class number formula used to verify computed values.
Engineering↗
Class Numbers of Imaginary Quadratic Fields
Computing 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 numbe…
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