{"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. 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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9912041","kind":"arxiv","version":3},"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"}