{"paper":{"title":"Anatomy of torsion in the CM case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abbey Bourdon, Paul Pollack, Pete L. Clark","submitted_at":"2015-06-01T16:52:52Z","abstract_excerpt":"Let $T_{\\mathrm{CM}}(d)$ denote the maximum size of a torsion subgroup of a CM elliptic curve over a degree $d$ number field. We initiate a systematic study of the asymptotic behavior of $T_{\\mathrm{CM}}(d)$ as an \"arithmetic function\". Whereas a recent result of the last two authors computes the upper order of $T_{\\mathrm{CM}}(d)$, here we determine the lower order, the typical order and the average order of $T_{\\mathrm{CM}}(d)$ as well as study the number of isomorphism classes of groups $G$ of order $T_{\\mathrm{CM}}(d)$ which arise as the torsion subgroup of a CM elliptic curve over a degre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00565","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"}