{
  "id": 3649,
  "curve_key": "19651219560054992273972627974801:-78689368785220532106987643118450877553168102201",
  "ainvs": [
    "1",
    "0",
    "0",
    "-409400407501145672374429749475",
    "91075658316227433599720258143475077076650625"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 216.16707657100704,
  "faltings_height": 15.986066748246417,
  "conductor": "177599378108948787912335962451915637757725844372530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "53",
    "59",
    "71",
    "73",
    "83",
    "107",
    "127",
    "463",
    "1069",
    "1231",
    "2879",
    "5547599",
    "16379591",
    "16791659"
  ],
  "discriminant": "808277286802827723504942151135272525682244753957703943066833547380231096051981542400000000",
  "regulator": "63230625934718757602.532952998583933132540709118192698487166255661398",
  "points": [
    [
      "-2335864005896935129745586309284290/4577138393556897961",
      "126582341530562225240314450610136186980650676336125/9792443305242158231251771541"
    ],
    [
      "-3715373275101014957436788050/7988983537441",
      "303697636377659203148802537494153593087975/22580694199922700239"
    ],
    [
      "-362050639803131808612994/9238093225",
      "9187296566565440473676110067365837859/887919330320875"
    ],
    [
      "-11793695147606852029090/152448409",
      "20814707151874450193847993771795355/1882280505923"
    ],
    [
      "-4283243745082981816450/15031129",
      "791774944740445679217558893884325/58275687133"
    ],
    [
      "-9701360227697093895119/89113600",
      "9750853930743964047723760556198759/841232384000"
    ],
    [
      "2798858178321520750/2209",
      "4161187146005479234094289575/103823"
    ],
    [
      "25004065108141168942/159201",
      "351666882944680178622652662919/63521199"
    ],
    [
      "43419043896221025902/160801",
      "30055346315835942653521815577/64481201"
    ],
    [
      "785852881184857361684/1481089",
      "8687004856134712864262184010531/1802485313"
    ],
    [
      "3837122899092591007550/16008001",
      "165963834110824936130665071978025/64048012001"
    ],
    [
      "143335895999980615957310/559369801",
      "22892321981730785223509142387907315/13229655163451"
    ],
    [
      "430057826317780571974400/362635849",
      "246432198431566791348182068112357125/6905674472507"
    ],
    [
      "119465119438878449676903550/28778747449",
      "1290991664718071927770975679373182033675/4882113053490707"
    ],
    [
      "568388326843547054465577609950/2344208697186841",
      "279512331533406381398373490330897139737214725/113499620473747499115389"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 471/107 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:26:46",
  "updated_at": "2026-09-29 19:26:46"
}