{"paper":{"title":"Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Stephan Baier, Vijay M. Patankar","submitted_at":"2017-10-05T17:31:01Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$. Let $p$ be a prime of good reduction for $E$. Then, for a prime $p \\neq \\ell$, the Frobenius automorphism associated to $p$ (unique up to conjugation) acts on the $\\ell$-adic Tate module of $E$. The characteristic polynomial of the Frobenius automorphism has rational integer coefficients and is independent of $\\ell$. Its splitting field is called the Frobenius field of $E$ at $p$. Let $E_1$ and $E_2$ be two elliptic curves defined over $\\mathbb{Q}$ that are non-isogenous over $\\overline{\\mathbb{Q}}$ and also without complex multiplication over $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02125","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"}