{"paper":{"title":"Torsion subgroups of rational elliptic curves over the compositum of all cubic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alvaro Lozano-Robledo, Andrew V. Sutherland, Filip Najman, Harris B. Daniels","submitted_at":"2015-09-02T00:10:16Z","abstract_excerpt":"Let $E/\\mathbb{Q}$ be an elliptic curve and let $\\mathbb{Q}(3^\\infty)$ be the compositum of all cubic extensions of $\\mathbb{Q}$. In this article we show that the torsion subgroup of $E(\\mathbb{Q}(3^\\infty))$ is finite and determine 20 possibilities for its structure, along with a complete description of the $\\overline{\\mathbb{Q}}$-isomorphism classes of elliptic curves that fall into each case. We provide rational parameterizations for each of the 16 torsion structures that occur for infinitely many $\\overline{\\mathbb{Q}}$-isomorphism classes of elliptic curves, and a complete list of $j$-inv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00528","kind":"arxiv","version":5},"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"}