Browsing by Author "Miller, Nicole Renee"
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- The Structure of the Class Group of Imaginary Quadratic FieldsMiller, Nicole Renee (Virginia Tech, 2005-05-11)Let Q(√(-d)) be an imaginary quadratic field with discriminant Δ. We use the isomorphism between the ideal class groups of the field and the equivalence classes of binary quadratic forms to find the structure of the class group. We determine the structure by combining two of Shanks' algorithms [7, 8]. We utilize this method to find fields with cyclic factors that have order a large power of 2, or fields with class groups of high 5-ranks or high 7-ranks.