{"paper":{"title":"On isogeny classes of Edwards curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.NT","authors_text":"Omran Ahmadi, Robert Granger","submitted_at":"2011-03-17T11:15:55Z","abstract_excerpt":"We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\\em complete} Edwards curve, and that an Edwards curve is isogenous to an {\\em original} Edwards curve over $\\F_q$ if and only if its group order is divisible by 8 if $q \\equiv -1 \\pmod{4}$, and 16 if $q \\equiv 1 \\pmod{4}$. Furthermore, we give formulae for the proportion of $d \\in \\F_q \\setminus \\{0,1\\}$ for which the Edwards curve $E_d$ is complete or original, relative to the total number of $d$ in each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3381","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"}