{
  "id": 6218,
  "curve_key": "0:-342162842656577127264",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "396021808630297601"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 94.56363689150307,
  "faltings_height": 5.937958983416884,
  "conductor": "5645997824789233996179850145748787236",
  "bad_primes": [
    "2",
    "3",
    "160481",
    "2467717727521"
  ],
  "discriminant": "-67751973897470807954158201748985446832",
  "regulator": "12490181499378.381221244063242044254337466056404116047750160205",
  "points": [
    [
      "-185548",
      "624206497"
    ],
    [
      "3208040",
      "5780279551"
    ],
    [
      "-24159480745/52441",
      "6558291741275564/12008989"
    ],
    [
      "7018106/169",
      "1382702895985/2197"
    ],
    [
      "66167758/289",
      "3138263464059/4913"
    ],
    [
      "123861455/2401",
      "74049657875276/117649"
    ],
    [
      "425046340/169",
      "8871429414453/2197"
    ],
    [
      "902652598/169",
      "27154674576951/2197"
    ],
    [
      "7820921111/6889",
      "779651390254720/571787"
    ],
    [
      "39539229935/9409",
      "7883118547162052/912673"
    ],
    [
      "43962454864/72361",
      "15330199360434795/19465109"
    ],
    [
      "266065563970/91809",
      "138352727920706477/27818127"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Generic-rank-4 Burkhardt fibration associated with quartic coordinates (5, 11, 74, -40, 130), specialized at t=-8054/3131. PARI/GP 2.17.4 returned rank bounds [12,12].",
  "created_at": "2026-10-30 22:12:12",
  "updated_at": "2026-10-30 22:12:12"
}