{
  "id": 1778,
  "curve_key": "876580658702102114422222454401:-818399475690500130063437954214258185739441601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-18262097056293794050462967800",
    "947221615382521776843113311413294620840000"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    8,
    2
  ],
  "naive_height": 206.837478703757,
  "faltings_height": 15.049095135147619,
  "conductor": "486370782457448070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "41",
    "61",
    "191",
    "353",
    "3271"
  ],
  "discriminant": "2188258744343393327073128208815979236032677046635246478348390767774386708505600000000",
  "regulator": "1821.7809156640199043787820072949472700491756",
  "points": [
    [
      "74021617782920",
      "31794425743000034480"
    ],
    [
      "81766735559600",
      "25797576413352528200"
    ],
    [
      "8775517172730787722056858700518960/117806438860954586521",
      "18243142868646417426484039651543006669780183825640/1278655473449200890038991093181"
    ]
  ],
  "submitter": "hdeping",
  "history": [
    {
      "kind": "rank_improved",
      "user": "hdeping",
      "old_rank": 2,
      "new_rank": 3,
      "at": "2026-09-25 14:39:16"
    }
  ],
  "commentary": "Specialization t=91/61 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4).",
  "created_at": "2026-09-25 14:35:37",
  "updated_at": "2026-09-25 14:39:16"
}