{"paper":{"title":"Computing the rational torsion of an elliptic curve using Tate normal form","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"I. Garc\\'ia, J.M. Tornero, M.A. Olalla Acosta","submitted_at":"2000-11-10T11:59:33Z","abstract_excerpt":"It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n ($4 \\leq n \\leq 10$, or n = 12) lie in a one-parameter family. However, this fact does not appear to have been used ever for computing the torsion of an elliptic curve. We present here a extremely down-to-earth algorithm using the existence of such a family."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011066","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"}