{
  "id": 1777,
  "curve_key": "123097460901862307714420641:668764982589777348503078511227140039439",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2564530435455464744050430",
    "-774033544664307864229665861908231100"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    8,
    2
  ],
  "naive_height": 180.22505591558954,
  "faltings_height": 13.070518230540152,
  "conductor": "132792596202630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "47",
    "73",
    "149",
    "193"
  ],
  "discriminant": "820629260378340122534707714306737863072565546605087122793887672400100000000",
  "regulator": "1707.2111411137934742190002124525324629851573",
  "points": [
    [
      "-557806133900",
      "694922703833151730"
    ],
    [
      "-2287973216290310660/6265009",
      "5290514967596142058182262990/15681317527"
    ],
    [
      "3484671356493652101640/949687489",
      "183279040738711134507748125258310/29266519348513"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Specialization t=47/18 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4). This is the Dujella (2001) rank-3 record curve, identified here as a specialization of the family.",
  "created_at": "2026-09-25 14:35:28",
  "updated_at": "2026-09-25 14:35:28"
}