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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0201008","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2002-01-01T22:34:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"520f89867a181efdebd9f70de2e05ee25db5580c3516c0972e13248a5d3c8e5e","abstract_canon_sha256":"7f71666ac03b494aa8b5d1afc18a2f468c39b096249c17515076caed51b5a381"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:32.316782Z","signature_b64":"uDzXWqbdRjV1buFQDH+2ZFhM0nOSD9MOMiSJnXQIj1JCCBtV6ZSLze4IjXW9tBsJoPZsFs/uWA2V0eBvL3rpBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4c28d96ad78ff7e2b80b5e34b9a6b5166cfff5fb9048fd353c813beb41f0456","last_reissued_at":"2026-05-18T03:45:32.316328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:32.316328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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