{
  "id": 6217,
  "curve_key": "0:5220600995229954696",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-6042362262997633"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 86.19828840469174,
  "faltings_height": 5.24084660951594,
  "conductor": "7211879845392172563924114983481",
  "bad_primes": [
    "3",
    "281947",
    "3174939899"
  ],
  "discriminant": "-15772381221872681397302039468872947",
  "regulator": "4571365706613629.51611767829853559560196403457207138423196959",
  "points": [
    [
      "677584139711217/3617541316",
      "5003909887266235053869/217580639992136"
    ],
    [
      "62960864649984753/127193516164",
      "-15399596372407163329371925/45362549991761288"
    ],
    [
      "1152472778276217/4045468816",
      "-33625254418912127617619/257307998572864"
    ],
    [
      "1270250924930385/5201005924",
      "-34633795269667336441133/375086145227032"
    ],
    [
      "1845722764659577/9667608976",
      "-28777946550718819354349/950557984956224"
    ],
    [
      "18026376852831225/66454652944",
      "2020983147300732024338221/17131212073127872"
    ],
    [
      "21016149473205625/73977472144",
      "2614595083851241563601171/20120984693502272"
    ],
    [
      "218313266354425631321169/23653563348122500",
      "102004309994774639654245616802582053/3637850630285698350875000"
    ],
    [
      "191943330556186831425/782094023811136",
      "2044761962630111358279605970529/21871997672636895952384"
    ],
    [
      "218022380647051137441/573073231346704",
      "3037469739017867806161807745519/13718770285400717027392"
    ],
    [
      "30712046503961381662961353/1614266179257213504",
      "-170201328075257081211011711792386381445/2050986122523089075156203008"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Generic-rank-4 Burkhardt fibration associated with quartic coordinates (8, 13, 31, 16, -14), specialized at t=8364/10145. PARI/GP 2.17.4 returned rank bounds [11,11].",
  "created_at": "2026-10-30 22:11:25",
  "updated_at": "2026-10-30 22:11:25"
}