{
  "id": 6000,
  "curve_key": "-58026353984:-176147206329835520",
  "ainvs": [
    "0",
    "-1",
    "0",
    "1208882375",
    "203873678439481"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 79.42019287992589,
  "faltings_height": 4.677101609054247,
  "conductor": "241967553632540594112",
  "bad_primes": [
    "2",
    "3",
    "17",
    "19",
    "41",
    "43",
    "683",
    "769",
    "1033",
    "4079"
  ],
  "discriminant": "-18068990962430051288513043591168",
  "regulator": "308541.90590831072227534040880737178575683636337208465638",
  "points": [
    [
      "-35315",
      "10823016"
    ],
    [
      "-25557",
      "12501392"
    ],
    [
      "-10376",
      "13791777"
    ],
    [
      "7899",
      "14625848"
    ],
    [
      "22741",
      "15592464"
    ],
    [
      "27415",
      "16050516"
    ],
    [
      "48448",
      "19394763"
    ],
    [
      "67841",
      "24456336"
    ],
    [
      "81945",
      "29209384"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of the rank-9 curve [0,-1,0,-45463157665,3604445187793921] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 544640.\r\n\r\nReduction gives the global minimal model [0,-1,0,1208882375,203873678439481]. 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 18:09:00",
  "updated_at": "2026-10-27 18:09:00"
}