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We study the Mordell-Weil torsion groups of cubic curves $C_s$ over $\\bfQ$ and $D_s$ over $\\bfQ(\\sqrt{-3})$ respectively. We show that $C_{s}$ has the torsion group $\\bf Z/3\\bf Z$ for a generic $s\\in \\bf Q$ and it also contains subfamilies which coincide with "},"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":"math/9912041","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-12-06T08:07:24Z","cross_cats_sorted":[],"title_canon_sha256":"87d27f090386c9f2a53ebb29cd8b15e9b8080e56b8ca5deff6b451b2a39a5358","abstract_canon_sha256":"43c044ec95b5510ea09d1ef538315f829f6b61f4f98c0b46836fcde8a847fbc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:32.301111Z","signature_b64":"Zc8pgkpH2aB9/whsFQVBZwmryq4DCY2vy74N65G5KABvOQflIf18fFxWgr/aTYjb4BZCaGdVsBTKfEVoJiQ2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef1383980b1fcdc824d15d5fda806e0240d1a09f7da91b40a6a5498513290efb","last_reissued_at":"2026-05-18T01:05:32.300420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:32.300420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic Curves from Sextics","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mutsuo Oka","submitted_at":"1999-12-06T08:07:24Z","abstract_excerpt":"Let $\\mathcal N$ be the moduli space of sextics with 3 (3,4)-cusps. The quotient moduli space ${\\mathcal N}/G$ is one-dimensional and consists of two components, ${\\mathcal N}_{torus}/G$ and ${\\mathcal N}_{gen}/G$. By quadratic transformations, they are transformed into one-parameter families $C_s$ and $D_s$ of cubic curves respectively. We study the Mordell-Weil torsion groups of cubic curves $C_s$ over $\\bfQ$ and $D_s$ over $\\bfQ(\\sqrt{-3})$ respectively. 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