Hatcher-Topology-of-Numbers · Problem 8.3.1

Quadratic Fields

Mathematics — Algebraic Topology · correspondence-forms-ideals

Problem

For discriminant Δ=−23\Delta = -23 draw the lattice LQL_Q for one form in each proper equivalence class of forms. Prove that no two of these lattices have the same shape by computing ratios of distances from the origin to nearby points in the lattice, with an extra argument to deal with mirror image lattices that do not have the same shape.

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