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We look for small (sometimes \"minimal\") set of generators of $K(\\mathcal{E}[m])$. For $m=3$ and $m=4$, we describe explicit generators, degree and Galois groups of the extensions $K(\\mathcal{E}[m])/K$."},"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":"1403.2572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-11T13:34:22Z","cross_cats_sorted":[],"title_canon_sha256":"d63c49365271034464b3876fe0ddd6ce357a158f0e7b3650f71f5b125403bcdd","abstract_canon_sha256":"684708d81efa587f5cb107f1e7a8569b99a2300733ac4e34359eaa541f6fad18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:27.351500Z","signature_b64":"5QndDCxYIeN0YJ4a1prpsQJ0S8Um/t0fvKgWqQUKEFeVCdEiRfOlIKEW/jR+92AV9gF9KXV+Cc9q1Zpu4hnhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"237fbaf9eb2c2d8af28272a8ed9e37988359c7c5f77e13d7a625a9bde69808af","last_reissued_at":"2026-05-18T01:58:27.350996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:27.350996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fields generated by torsion points of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Bandini, Laura Paladino","submitted_at":"2014-03-11T13:34:22Z","abstract_excerpt":"Let K be a number field and let $\\mathcal{E}$ be an elliptic curve defined over $K$. 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