{
  "id": 6227,
  "curve_key": "0:-48713755767383646084600",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "56381661767805145931"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 104.48049680473716,
  "faltings_height": 6.7643639761863925,
  "conductor": "2215564848694462660775701182225",
  "bad_primes": [
    "3",
    "5",
    "7",
    "13",
    "37",
    "593",
    "5737",
    "8663"
  ],
  "discriminant": "-1373281250558045973160583115795502841641875",
  "regulator": "472380791.728246197283025407711908903065061567320696861468045",
  "points": [
    [
      "-3585855",
      "3205224067"
    ],
    [
      "-3350165",
      "4333674117"
    ],
    [
      "-2287155",
      "6664636192"
    ],
    [
      "147889",
      "7508987699"
    ],
    [
      "170755",
      "7509103842"
    ],
    [
      "829725",
      "7546713232"
    ],
    [
      "4595955",
      "12387942157"
    ],
    [
      "13316485",
      "49170902007"
    ],
    [
      "13407135",
      "49662170617"
    ],
    [
      "29141385",
      "157492342507"
    ],
    [
      "129989769/16",
      "1558018169221/64"
    ]
  ],
  "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].",
  "created_at": "2026-10-31 08:48:28",
  "updated_at": "2026-10-31 08:48:28"
}