{
  "id": 5994,
  "curve_key": "410227240864:240370466102939008",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-8546400851",
    "-278203709189229"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 80.21993126735079,
  "faltings_height": 4.65077640513767,
  "conductor": "1488768414305232128640",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "53",
    "107",
    "167",
    "13101841"
  ],
  "discriminant": "6514872754716458457055963964160",
  "regulator": "21885643.204208183055942606828784758243279255809308404834",
  "points": [
    [
      "-40350",
      "973239"
    ],
    [
      "-157604390/2601",
      "549740146519/132651"
    ],
    [
      "-76746998/1369",
      "251856689543/50653"
    ],
    [
      "-27917534/625",
      "59338237889/15625"
    ],
    [
      "-24701615/576",
      "42463066681/13824"
    ],
    [
      "-21616958/529",
      "20347159073/12167"
    ],
    [
      "8901457/64",
      "17910216647/512"
    ],
    [
      "9885922/49",
      "27029097983/343"
    ],
    [
      "10739125/36",
      "33265574299/216"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of [0,-1,0,-30426475321,1732229429427145] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 544909.\r\n\r\nReduction gives the global minimal model [0,-1,0,-8546400851,-278203709189229]. PARI/GP returned matching rank bounds [9,9] and the nine rational points listed here. All nine were checked exactly on this model. Rational torsion Z/2Z.\r\n\r\nSource:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz",
  "created_at": "2026-10-27 17:28:20",
  "updated_at": "2026-10-27 17:28:20"
}