{"paper":{"title":"On several families of elliptic curves with arbitrary large Selmer groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Derong Qiu, Fei Li","submitted_at":"2009-11-02T05:33:29Z","abstract_excerpt":"In this paper, we calculate the $ \\phi (\\hat{\\phi})-$Selmer groups $ S^{(\\phi)} (E / \\Q) $ and $ S^{(\\hat{\\varphi})} (E^{\\prime} / \\Q) $ of elliptic curves $ y^{2} = x (x + \\epsilon p D) (x + \\epsilon q D) $ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0236","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"}