{
  "id": 5989,
  "curve_key": "-1138542593246144:-8271342345271840330240",
  "ainvs": [
    "0",
    "1",
    "0",
    "23719637359295",
    "9573320806165971999"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 104.00557623736533,
  "faltings_height": 6.73891488571691,
  "conductor": "319122928903483888205248",
  "bad_primes": [
    "2",
    "31",
    "41",
    "113",
    "193",
    "233",
    "241",
    "257",
    "1783",
    "6991"
  ],
  "discriminant": "-893683002223945081473645244074846240636928",
  "regulator": "13826828666.36350920396497873487735829941175594821260644518",
  "points": [
    [
      "26618317",
      "139645819004"
    ],
    [
      "1801369",
      "7625382632"
    ],
    [
      "262161829/25",
      "4696184505508/125"
    ],
    [
      "55716493/4",
      "441271063693/8"
    ],
    [
      "5286312241/1369",
      "638191985193464/50653"
    ],
    [
      "6963781/4",
      "59943721879/8"
    ],
    [
      "9125065921/2809",
      "1637022741432064/148877"
    ],
    [
      "5616421/4",
      "54049695559/8"
    ],
    [
      "7748367961/400",
      "703711046487259/8000"
    ],
    [
      "129501169/25",
      "2059421089672/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogenous partner of curve#5891.\r\n\r\nThe source points come from Michael Rubinstein’s elliptic-curves-by-rank repository, rank_10.add_2026-10-24.tsv.gz, 4929th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b:\r\nhttps://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_10.add_2026-10-24.tsv.gz\r\n\r\nStarting from [0,1,0,-6080575076865,1210755392118316639], I transported the ten supplied independent rational points through the rational degree-2 isogeny and then to the global minimal model displayed here. All ten points were checked exactly. Independence is preserved under the isogeny, establishing rank at least 10. The rational torsion subgroup is Z/2. Conductor 319122928903483888205248.\r\n\r\nThe construction author and search method are not identified in the source row.",
  "created_at": "2026-10-27 16:53:24",
  "updated_at": "2026-10-27 16:53:24"
}