{"paper":{"title":"Rank of elliptic curves associated to the Brahmagupta quadrilaterals","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Arman Shamsi Zargar, Farzali Izadi, Foad Khoshnam","submitted_at":"2015-02-09T10:28:31Z","abstract_excerpt":"In this paper, we construct a family of elliptic curves of rank at least five. To do so, we use the Brahmagupta formula for the area of cyclic quadrilaterals $(p^3,q^3,r^3,q^3)$ not necessarily standing for the genuine sides of quadrilaterals. It turns out that, as parameters of the curves, the integers $p,q,r,s$, along with the extra integers $u$, $v$ satisfy $u^6+v^6+p^6+q^6=2(r^6+s^6)$, $uv=pq$. However, we utilize a subset of the solutions of the above system via the rational points of a specific elliptic curve of positive rank lying on the system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02418","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":""},"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"}