{"paper":{"title":"Elliptic curves with maximally disjoint division fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Harris B. Daniels, James Ricci, Jeffrey Hatley","submitted_at":"2015-07-27T14:48:59Z","abstract_excerpt":"One of the many interesting algebraic objects associated to a given rational elliptic curve, $E$, is its full-torsion representation $\\rho_E:\\mathrm{Gal}(\\bar{\\mathbf{Q}}/\\mathbf{Q})\\to\\mathrm{GL}_2(\\hat{\\mathbf{Z}})$. Generalizing this idea, one can create another full-torsion Galois representation, $\\rho_{(E_1,E_2)}:\\mathrm{Gal}(\\bar{\\mathbf{Q}}/\\mathbf{Q})\\to\\left(\\mathrm{GL}_2(\\hat{\\mathbf{Z}})\\right)^2$ associated to a pair $(E_1,E_2)$ of rational elliptic curves. The goal of this paper is to provide an infinite number of concrete examples of pairs of elliptic curves whose associated full"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07423","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"}