{"paper":{"title":"Growth of the analytic rank of modular elliptic curves over quintic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michele Fornea","submitted_at":"2018-02-20T19:15:15Z","abstract_excerpt":"Given $F$ a totally real field and $E_{/F}$ a modular elliptic curve, we denote by $G_5(E_{/F};X)$ the number of quintic extensions $K$ of $F$ such that the norm of the relative discriminant is at most $X$ and the analytic rank of $E$ grows over $K$, i.e., $r_\\mathrm{an}(E/K)>r_\\mathrm{an}(E/F)$. We show that $G_5(E_{/F};X)\\asymp_{+\\infty} X$ when the elliptic curve $E_{/F}$ has odd conductor and at least one prime of multiplicative reduction. As Bhargava, Shankar and Wang \\cite{BSW} showed that the number of quintic extensions of $F$ with norm of the relative discriminant at most $X$ is asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07290","kind":"arxiv","version":2},"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"}