{"paper":{"title":"Isogenies of non-CM elliptic curves with rational $j$-invariants over number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Filip Najman","submitted_at":"2015-06-09T23:01:42Z","abstract_excerpt":"We unconditionally determine $I_\\Q(d)$, the set of possible prime degrees of cyclic $K$-isogneies of elliptic curves with $\\Q$-rational $j$-invariants and without complex multiplication over number fields $K$ of degree $\\leq d$, for $d\\leq 7$, and give an upper bound for $I_\\Q(d)$ for $d>7$. Assuming Serre's uniformity conjecture, we determine $I_\\Q(d)$ exactly for all positive integers $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03127","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"}