{
  "id": 1781,
  "curve_key": "3287926687220757121:-5699818521148702468715398081",
  "ainvs": [
    "1",
    "0",
    "0",
    "-68498472650432440",
    "6597012171547236617921600"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8,
    2
  ],
  "naive_height": 127.91036656129258,
  "faltings_height": 8.592419053016659,
  "conductor": "44245640670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "47",
    "89",
    "241"
  ],
  "discriminant": "1768561927045055047002658300206667798876185600000000",
  "regulator": "40.0419017847502058231867871116711343058457",
  "points": [
    [
      "33900142628/289",
      "2061207821164888/4913"
    ],
    [
      "21526744060910/73441",
      "68081967084010895180/19902511"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Specialization t=15/4 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4).",
  "created_at": "2026-09-25 14:35:56",
  "updated_at": "2026-09-25 14:35:56"
}