{"paper":{"title":"The truth about torsion in the CM case, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Pollack, Pete L. Clark","submitted_at":"2016-12-19T19:26:03Z","abstract_excerpt":"Let $T_{{\\rm CM}}(d)$ be the largest size of the torsion subgroup of an elliptic curve with complex multiplication (CM) defined over a degree $d$ number field. Work of Breuer and Clark--Pollack showed $\\limsup_{d \\to \\infty} \\frac{T_{{\\rm CM}}(d)}{d \\log \\log d} \\in (0,\\infty)$. Here we show that the above limit supremum is precisely $\\frac{e^{\\gamma} \\pi}{\\sqrt{3}}$. We also study -- in part, out of necessity -- the upper order of the size of the torsion subgroup of various restricted classes of CM elliptic curves over number fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06318","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"}