{"paper":{"title":"On a local invariant of elliptic curves with a p-isogeny","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Matthew Gealy, Zev Klagsbrun","submitted_at":"2017-03-06T23:47:10Z","abstract_excerpt":"An elliptic curve $E$ defined over a $p$-adic field $K$ with a $p$-isogeny $\\phi:E\\rightarrow E^\\prime$ comes equipped with an invariant $\\alpha_{\\phi/K}$ that measures the valuation of the leading term of the formal group homomorphism $\\Phi:\\hat E \\rightarrow \\hat E^\\prime$. We prove that if $K/\\mathbb{Q}_p$ is unramified and $E$ has additive, potentially supersingular reduction, then $\\alpha_{\\phi/K}$ is determined by the number of distinct geometric components on the special fibers of the minimal proper regular models of $E$ and $E^\\prime$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02148","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"}