{"paper":{"title":"On the torsion of rational elliptic curves over sextic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Enrique Gonz\\'alez-Jim\\'enez, Harris B. Daniels","submitted_at":"2018-08-08T13:40:04Z","abstract_excerpt":"Given an elliptic curve $E/\\mathbb{Q}$ with torsion subgroup $G = E(\\mathbb{Q})_{\\rm tors}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of $\\mathbb{Q}$. We also determine which groups $H = E(K)_{\\rm tors}$ can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth of over sextic fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02887","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.02887/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}