{"paper":{"title":"Elliptic Curves with Isomorphic Groups of Points over Finite Field Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Clemens Heuberger, Michela Mazzoli","submitted_at":"2016-05-11T15:24:49Z","abstract_excerpt":"Consider a pair of ordinary elliptic curves $E$ and $E'$ defined over the same finite field $\\mathbb{F}_q$. Suppose they have the same number of $\\mathbb{F}_q$-rational points, i.e. $|E(\\mathbb{F}_q)|=|E'(\\mathbb{F}_q)|$. In this paper we characterise for which finite field extensions $\\mathbb{F}_{q^k}$, $k\\geq 1$ (if any) the corresponding groups of $\\mathbb{F}_{q^k}$-rational points are isomorphic, i.e. $E(\\mathbb{F}_{q^k}) \\cong E'(\\mathbb{F}_{q^k})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03474","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"}