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We determine conditions on the discriminant of $f$ that are equivalent to the existence of an unramified lift $\\widetilde{f}:\\text{Gal}(\\overline{\\mathbf{Q}}/\\mathbf{Q})\\rightarrow E$ of $f$.\n  As a consequence of this result, we use conditions on the discriminant of $K$ for $K/\\mathbf{Q}$ abelian to classify and count unramified nonabelian"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.00900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-02T20:39:40Z","cross_cats_sorted":[],"title_canon_sha256":"806c4dcffd233211932d111a5509b95c3aa6887d31f9fe918873d0de15e3c06b","abstract_canon_sha256":"56bb778944947471f8ae64f407ac46dd4b7c68f82c556305e36607d1b264222a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:47.541103Z","signature_b64":"+rZay6P5NUNYj0S2Rg/qgcgGeFMXB3BpJDD95mb5RVlmfD7En62qWfZ5MUZ+SktR14lLb9c4cC4LNXE1qCk7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"870d9635587e3b29aae9c09d92afae9f45d782af35b625315a1b36f08fbdf70a","last_reissued_at":"2026-05-18T00:33:47.540614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:47.540614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brandon Alberts","submitted_at":"2017-10-02T20:39:40Z","abstract_excerpt":"We study solutions to the Brauer embedding problem with restricted ramification. 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