{"paper":{"title":"On the number of equivalence classes of binary forms of given degree and given discriminant","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Attila Berczes, Jan-Hendrik Evertse, Kalman Gyory","submitted_at":"2003-12-11T11:48:00Z","abstract_excerpt":"We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for the number of irreducible binary forms with rational integral coefficients with given invariant order. Our bounds depend on as few parameters as possible. For instance, we show that the number of equivalence classes of irreducible binary forms with rational integral coefficients of degree r with given invariant order has an upper bound depending only on r. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312234","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"}