{"paper":{"title":"A note on the procedure to find the generic polynomial of a quotient (closely following Adelmann)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rachel Davis","submitted_at":"2018-05-10T16:15:24Z","abstract_excerpt":"There are 3 examples in these notes. The first one is the standard example of the cubic resolvent of a quartic. The second example is exactly from Adelmann \\cite{Adelmann} and gives a defining polynomial corresponding to the unique $S_4$-quotient of $\\mathrm{GL}_2(\\mathbb{Z}/4\\mathbb{Z})$. The splitting field of the Adelmann polynomial over $\\mathbb{Q}$ is a subfield of the 4-division field of an elliptic curve, that contains the 2-division field of the elliptic curve. The third example is new and needed in the study of the field theory of quaternion origami. Associated to an elliptic curve de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04042","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}