{"paper":{"title":"Fast algorithms for computing isogenies between elliptic curves","license":"","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"cs.CC","authors_text":"Alin Bostan (INRIA Rocquencourt), Bruno Salvy (INRIA Rocquencourt), Eric Schost (LIX), Francois Morain (LIX, INRIA Futurs)","submitted_at":"2006-09-06T12:10:17Z","abstract_excerpt":"We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\\ell$ ($\\ell$ different from the characteristic) in time quasi-linear with respect to $\\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\\wp$-function and related functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0609020","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"}