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In particular we prove that the aforementioned set is empty unless $\\frac{\\alpha}{\\beta}\\in\\{-2,-\\frac{1}{2}\\"},"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":"1507.07047","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-25T01:07:09Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f1ca90cadd14c6df9199cd0cee51117ef8ccc63deb51a5e125ea7d117e3915d7","abstract_canon_sha256":"1d23d70954deb37d541e83127031b08441f05871b14d3b2a857083339aebdc5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:59.993062Z","signature_b64":"iA0p+nzLCHbaLqB9TBu7ezYixxp7z2oteSvgDMKMg/tqgcyhRQqpFTj+7Y0RmVLNt8BEZkYE6mMJ576WaW4vCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7afbc2170d4c0c3e11ac8c7d3ca49084043e3abceeb24b6e2621fcecef35eb4f","last_reissued_at":"2026-05-18T01:10:59.992627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:59.992627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Impossible intersections in a Weierstrass family of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Niki Myrto Mavraki","submitted_at":"2015-07-25T01:07:09Z","abstract_excerpt":"Consider the Weierstrass family of elliptic curves $E_{\\lambda}:y^2=x^3+\\lambda$ parametrized by nonzero $\\lambda\\in\\overline{\\mathbb{Q}_2}$, and let $P_{\\lambda}(x)=(x,\\sqrt{x^3+\\lambda})\\in E_{\\lambda}$. In this article, given $\\alpha,\\beta\\in\\overline{\\mathbb{Q}_2}$ such that $\\frac{\\alpha}{\\beta}\\in\\mathbb{Q}$, we provide an explicit description for the set of parameters $\\lambda$ such that $P_{\\lambda}(\\alpha)$ and $P_{\\lambda}(\\beta)$ are simultaneously torsion for $E_{\\lambda}$. 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