{"paper":{"title":"Iwasawa theory and ranks of elliptic curves in quadratic twist families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anwesh Ray, Jeffrey Hatley","submitted_at":"2024-12-10T08:44:19Z","abstract_excerpt":"We study the distribution of ranks of elliptic curves in quadratic twist families using Iwasawa-theoretic methods, contributing to the understanding of Goldfeld's conjecture. Given an elliptic curve $ E/\\mathbb{Q} $ with good ordinary reduction at $ 2 $ and $ \\lambda_2(E/\\mathbb{Q}) = 0 $, we use Matsuno's Kida-type formula to construct quadratic twists $ E^{(d)} $ such that $ \\lambda_2(E^{(d)}/\\mathbb{Q}) $ remains unchanged or increases by $ 2 $. When the root number of $E^{(d)}$ is $-1$ and the Tate-Shafarevich group $Sha(E^{(d)}/\\mathbb{Q})[2^\\infty] $ is finite, this yields quadratic twis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.07308","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.07308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}