{
  "id": 5641,
  "curve_key": "0:-8824962461249678630756053177389708365659776",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "10214076922742683600412098584941792089884"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 197.77231650975494,
  "faltings_height": 14.538682284937874,
  "conductor": "1287992189922279616434391982992675411341005002930125590555730451717037930063376",
  "bad_primes": [
    "2",
    "3",
    "401",
    "1201",
    "196375809688292829164869970064773"
  ],
  "discriminant": "-45069422709760408338272244268879697993644447062530954664726119966482591248777652992",
  "regulator": "4560850669596653123947.2839472155444997380181107198846937101502138684250155",
  "points": [
    [
      "-21652808368755",
      "7892100391708490247"
    ],
    [
      "-9854441545755",
      "96213886342323047253"
    ],
    [
      "7225262160306",
      "102913883877020459850"
    ],
    [
      "-3849056858622",
      "100782201933718648506"
    ],
    [
      "69637522047090",
      "589841669725718453622"
    ],
    [
      "123572700422245",
      "1377387180706732352747"
    ],
    [
      "19878763092649/4",
      "813361124524639254805/8"
    ],
    [
      "56194807750737/4",
      "911677606052418486873/8"
    ],
    [
      "385016132690521/16",
      "9945383762345233600675/64"
    ],
    [
      "-516913375504451/25",
      "4634219309061454640657/125"
    ],
    [
      "1308681389864749/25",
      "48999022258462444687193/125"
    ],
    [
      "42299376732650005/9",
      "8699633835814451608106669/27"
    ],
    [
      "76053773064421753/16",
      "20973995349582934818387379/64"
    ],
    [
      "9142824626056410/289",
      "1005387016864680119242386/4913"
    ],
    [
      "19240938228165529/400",
      "2788720124181945673670333/8000"
    ],
    [
      "-29039195056474398/4489",
      "29991012836170762212096402/300763"
    ],
    [
      "-486125058851751950/52441",
      "1165397594079687063294234158/12008989"
    ],
    [
      "22873662331470946698/58081",
      "109405679363324934633653856606/13997521"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "Specialization at (a, b, c, d, T) = (-7/8, -5/8, -1/4, 3/16, 2822744/6978815) of the rank-4 universal family described in curve#5569.",
  "created_at": "2026-10-24 00:23:59",
  "updated_at": "2026-10-24 00:23:59"
}