{"paper":{"title":"Genus 2 curves with (3,3)-split Jacobian and large automorphism group","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"T. Shaska","submitted_at":"2002-01-01T22:34:31Z","abstract_excerpt":"Let $\\C$ be a genus 2 curve defined over $k$, $char (k) =0$. If $\\C$ has a $(3,3)$-split Jacobian then we show that the automorphism group $Aut(\\C)$ is isomorphic to one of the following: $\\bZ_2, V_4, D_8$, or $D_{12}$. There are exactly six $\\bC$-isomorphism classes of genus two curves $\\C$ with $Aut(\\C)$ isomorphic to $D_8$ (resp., $D_{12}$). %We compute their absolute invariants $i_1, i_2, i_3$. We show that exactly four (resp., three) of these classes with group $D_8$ (resp., $D_{12}$) have representatives defined over $\\bQ$. We discuss some of these curves in detail and find their rationa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201008","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"}