{
  "id": 3636,
  "curve_key": "39251163964851319611239991121:-8030613301934242164467972648775694611022169",
  "ainvs": [
    "1",
    "1",
    "1",
    "-817732582601069158567499815",
    "9294691321682809931409995675785428600797"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 197.58366961424522,
  "faltings_height": 14.382360245978575,
  "conductor": "142345695678637990158711155259549347070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "41",
    "43",
    "61",
    "71",
    "89",
    "101",
    "107",
    "241",
    "439",
    "607",
    "2203",
    "2447",
    "75037"
  ],
  "discriminant": "-2325400601197026866769054026736995379255314916994583455181126401087272284160000000",
  "regulator": "34948568724930.17615654503194164794372280016036127466468845097663",
  "points": [
    [
      "-32125316545493",
      "49093064295994145946"
    ],
    [
      "-30680015895133",
      "74194116435422433906"
    ],
    [
      "-20131942379573",
      "132656931772193654106"
    ],
    [
      "16993362554837",
      "17490350397031078386"
    ],
    [
      "18259099096907",
      "21239527677838304346"
    ],
    [
      "107582018835707",
      "1080029531343693169146"
    ],
    [
      "333358188622243/9",
      "4662694715294001126782/27"
    ],
    [
      "20322673562771603/1369",
      "1046592310395283200252978/50653"
    ],
    [
      "21833417777310437/841",
      "1819045154717885721773994/24389"
    ],
    [
      "1200179143607378467/84681",
      "578941653401145215323435966/24642171"
    ],
    [
      "3389457379306819627/40401",
      "5918480260584382539640401466/8120601"
    ],
    [
      "3903463771915938323/458329",
      "16847399168896210707668929458/310288733"
    ],
    [
      "4884479909441928667/269361",
      "2895810411952166941768109974/139798359"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 311/126 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 19:24:06",
  "updated_at": "2026-09-29 19:24:06"
}