{"paper":{"title":"The average number of integral points on elliptic curves is bounded","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Levent Alpoge","submitted_at":"2014-12-02T20:07:01Z","abstract_excerpt":"We prove that, when elliptic curves $E/\\mathbb{Q}$ are ordered by height, the average number of integral points $\\#|E(\\mathbb{Z})|$ is bounded, and in fact is less than $66$ (and at most $\\frac{8}{9}$ on the minimalist conjecture). By \"$E(\\mathbb{Z})$\" we mean the integral points on the corresponding quasiminimal Weierstrass model $E_{A,B}: y^2 = x^3 + Ax + B$ with which one computes the na\\\"{\\i}ve height. The methods combine ideas from work of Silverman, Helfgott, and Helfgott-Venkatesh with work of Bhargava-Shankar and a careful analysis of local heights for \"most\" elliptic curves. The same "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1047","kind":"arxiv","version":3},"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"}