{"paper":{"title":"Elliptic curves over Hasse pairs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.NT","authors_text":"Antoine Joux, Daniele Taufer, Eleni Agathocleous","submitted_at":"2024-06-05T15:59:30Z","abstract_excerpt":"We call a pair of distinct prime powers $(q_1,q_2) = (p_1^{a_1},p_2^{a_2})$ a Hasse pair if $|\\sqrt{q_1}-\\sqrt{q_2}| \\leq 1$. For such pairs, we study the relation between the set $\\mathcal{E}_1$ of isomorphism classes of elliptic curves defined over $\\mathbb{F}_{q_1}$ with $q_2$ points, and the set $\\mathcal{E}_2$ of isomorphism classes of elliptic curves over $\\mathbb{F}_{q_2}$ with $q_1$ points. When both families $\\mathcal{E}_i$ contain only ordinary elliptic curves, we prove that their isogeny graphs are isomorphic. When supersingular curves are involved, we describe which curves might be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03399","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.03399/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}