{"paper":{"title":"Supersingular zeros of divisor polynomials of elliptic curves of prime conductor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Kohen, Matija Kazalicki","submitted_at":"2016-11-17T10:17:56Z","abstract_excerpt":"For a prime number $p$ we study the zeros modulo $p$ of divisor polynomials of rational elliptic curves $E$ of conductor $p$. Ono made the observation that these zeros of are often $j$-invariants of supersingular elliptic curves over $\\overline{\\mathbb{F}_p}$. We show that these supersingular zeros are in bijection with zeros modulo $p$ of an associated quaternionic modular form $v_E$.\n  This allows us to prove that if the root number of $E$ is $-1$ then all supersingular $j$-invariants of elliptic curves defined over $\\mathbb{F}_{p}$ are zeros of the corresponding divisor polynomial.\n  If the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05623","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"}