{
  "id": 6228,
  "curve_key": "0:1804213176569764669800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-2088209695103894294"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 97.8888230727285,
  "faltings_height": 6.215057831852337,
  "conductor": "2215564848694462660775701182225",
  "bad_primes": [
    "3",
    "5",
    "7",
    "13",
    "37",
    "593",
    "5737",
    "8663"
  ],
  "discriminant": "-1883787723673588440549496729486286476875",
  "regulator": "83680840112283.6291100961018999415264512664614661594869184798",
  "points": [
    [
      "7815483166/5041",
      "458130271671671/357911"
    ],
    [
      "663070907776/356409",
      "443831932874004677/212776173"
    ],
    [
      "455836957234/100489",
      "304299443301697958/31855013"
    ],
    [
      "3362053063828174/2934369",
      "-194942640928026112811279/5026574097"
    ],
    [
      "38992159581064/45369",
      "-243481480127650602674/9663597"
    ],
    [
      "482593294114/13225",
      "-335245218351621638/1520875"
    ],
    [
      "14052749656/8281",
      "-1260675903590069/753571"
    ],
    [
      "9127612443226/5631129",
      "19687024614441281005/13362669117"
    ],
    [
      "19401465637324/11909401",
      "61446944956556717419/41099342851"
    ],
    [
      "1087825312246/332929",
      "1100106002999100865/192100033"
    ],
    [
      "3397946495736601/2649778576",
      "19538897028219324932963/136400001978176"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Bruin–Nasserden rational parametrization of the Burkhardt quartic with parameters (u,v,w)=(5/4,1/4,15/8), specialized at t=-51/572. PARI/GP 2.17.4 returned rank bounds [11,11] for the source curve and its isogenous partner has eleven independent rational points.",
  "created_at": "2026-10-31 08:48:41",
  "updated_at": "2026-10-31 08:48:41"
}