{"paper":{"title":"Elliptic subfields and automorphisms of genus 2 function fields","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Helmut Voelklein, Tony Shaska","submitted_at":"2001-07-19T23:58:42Z","abstract_excerpt":"We study genus 2 function fields with elliptic subfields of degree 2. The locus $\\L_2$ of these fields is a 2-dimensional subvariety of the moduli space $\\mathcal M_2$ of genus 2 fields. An equation for $\\L_2$ is already in the work of Clebsch and Bolza. We use a birational parameterization of $\\L_2$ by affine 2-space to study the relation between the j-invariants of the degree 2 elliptic subfields. This extends work of Geyer, Gaudry, Stichtenoth and others. We find a 1-dimensional family of genus 2 curves having exactly two isomorphic elliptic subfields of degree 2; this family is parameteriz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107142","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"}