{
  "id": 1178,
  "curve_key": "22385344303588003970281:1267277143883246924994687467794571",
  "ainvs": [
    "1",
    "0",
    "1",
    "-466361339658083416048",
    "-1466755953607436274826469298322"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 154.3880802763358,
  "faltings_height": 10.924583482312125,
  "conductor": "783917988850972810230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "31",
    "37",
    "53",
    "103",
    "383",
    "487",
    "107053"
  ],
  "discriminant": "5562144759605538220635705466429765263015593914775496606636858000",
  "regulator": "40576862.67827447377479229407212767722663765023147677",
  "points": [
    [
      "-8185497083",
      "-1342454766599125"
    ],
    [
      "-3545927963",
      "377285039973035"
    ],
    [
      "3071224813806433/16129",
      "-169086943278163373458735/2048383"
    ],
    [
      "1864353018322",
      "-2545441953737743513"
    ],
    [
      "-26728336708574/1849",
      "-119367940705874468155/79507"
    ],
    [
      "-2229098332709726/156025",
      "-93057369581579247073358/61629875"
    ],
    [
      "-1043832400164926/201601",
      "-81422561709074061018665/90518849"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1121 and mapping all 7 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:38:30",
  "updated_at": "2026-09-23 21:38:30"
}