{"paper":{"title":"Neighborhood of the supersingular elliptic curve isogeny graph at $j=0$ and $1728$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Songsong Li, Yi Ouyang, Zheng Xu","submitted_at":"2019-05-01T10:12:55Z","abstract_excerpt":"We describe the neighborhood of the vertex $[E_0]$ (resp. $[E_{1728}]$) in the $\\ell$-isogeny graph $\\mathcal{G}_\\ell(\\mathbb{F}_{p^2}, -2p)$ of supersingular elliptic curves over the finite field $\\mathbb{F}_{p^2}$ when $p>3\\ell^2$ (resp. $p>4\\ell^2$) with $E_0: y^2=x^3+1$ (resp. $E_{1728}: y^2=x^3+x$) supersingular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00244","kind":"arxiv","version":2},"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"}