{"paper":{"title":"A Family of Elliptic Curves with a Lower Bound on 2-Selmer Ranks of Quadratic Twists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zev Klagsbrun","submitted_at":"2012-01-25T22:50:52Z","abstract_excerpt":"For any number field K with a complex place, we present an infinite family of elliptic curves defined over K such that $dim \\mathbb{F}_2 Sel_2(E^F/K) \\ge dim \\mathbb{F}_2 E^F(K)[2] + r_2$ for every quadratic twist E^F of every curve E in this family, where r_2 is the number of complex places of K. This provides a counterexample to a conjecture appearing in work of Mazur and Rubin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5407","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"}