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We give a new geometric description of when an element of the class group of a quadratic field, thought of as a quadratic form q, is n-torsion. We show that q corresponds to an n-torsion element if and only if there exists a degree n polynomial whose resultant with q is ± 1. This is motivated by a more precise geometric parameterization which directly connects torsion in class groups of quadratic fields to Selmer groups of singular genus 1 curves.arXiv:2106.10357v1 fatcat:zznikij2zrak5eneq7roggfjoy