{"paper":{"title":"Genus two curves covering elliptic curves: a computational approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"T. Shaska","submitted_at":"2012-09-14T13:37:16Z","abstract_excerpt":"A genus 2 curve $C$ has an elliptic subcover if there exists a degree $n$ maximal covering $\\psi: C \\to E$ to an elliptic curve $E$. Degree $n$ elliptic subcovers occur in pairs $(E, E')$. The Jacobian $J_C$ of $C$ is isogenous of degree $n^2$ to the product $E \\times E'$. We say that $J_C$ is $(n, n)$-split. The locus of $C$, denoted by $\\L_n$, is an algebraic subvariety of the moduli space $\\M_2$. The space $\\L_2$ was studied in Shaska/V\\\"olklein and Gaudry/Schost. The space $\\L_3$ was studied in Shaska (2004) were an algebraic description was given as sublocus of $\\M_2$.\n  In this survey we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3187","kind":"arxiv","version":1},"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"}