{"paper":{"title":"Injectivity of the specialization homomorphism of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ivica Gusi\\'c, Petra Tadi\\'c","submitted_at":"2014-09-25T09:07:28Z","abstract_excerpt":"Let $E:y^2=x^3+Ax^2+Bx+C$ be a nonconstant elliptic curve over $\\mathbb{Q}(t)$ with at least one nontrivial $\\mathbb{Q}(t)$-rational $2$-torsion point. We describe a method for finding $t_0\\in\\mathbb Q$ for which the corresponding specialization homomorphism $t\\mapsto t_0\\in\\mathbb{Q}$ is injective. The method can be directly extended to elliptic curves over $K(t)$ for a number field $K$ of class number $1$, and in principal for arbitrary number field $K$. One can use this method to calculate the rank of elliptic curves over $\\mathbb Q(t)$ of the form as above, and to prove that given points a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7189","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"}