{
  "id": 5995,
  "curve_key": "-115456326687:-175195582375358961",
  "ainvs": [
    "1",
    "-1",
    "1",
    "2405340139",
    "202772063451260"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 79.40935871668512,
  "faltings_height": 4.681178553858749,
  "conductor": "80438488494668794269",
  "bad_primes": [
    "3",
    "13",
    "61",
    "131",
    "179",
    "367",
    "1093",
    "1511"
  ],
  "discriminant": "-18653092465808033563691792211183",
  "regulator": "916999.02138933375736162488281155479923445459497026926410",
  "points": [
    [
      "-178293/4",
      "21343913/8"
    ],
    [
      "-38262",
      "7416631"
    ],
    [
      "-32187",
      "9608005"
    ],
    [
      "-31086",
      "9912982"
    ],
    [
      "19887/4",
      "117243215/8"
    ],
    [
      "73876",
      "27956904"
    ],
    [
      "83418",
      "31325230"
    ],
    [
      "156084",
      "66109123"
    ],
    [
      "1113954",
      "1176379543"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of [1,-1,1,-40537739066,2932199823257696] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 544601.\r\n\r\nReduction gives the global minimal model [1,-1,1,2405340139,202772063451260]. 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 17:33:23",
  "updated_at": "2026-10-27 17:33:23"
}