{
  "id": 5472,
  "curve_key": "0:668209416541633800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-773390528404669"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 82.08675603426795,
  "faltings_height": 4.898218911980624,
  "conductor": "10335736674882191357895573456075",
  "bad_primes": [
    "3",
    "5",
    "47",
    "1129",
    "777330623"
  ],
  "discriminant": "-258393416872054783947389336401875",
  "regulator": "309272542397.5874435286236396176865705105338270086241829166",
  "points": [
    [
      "2036209/16",
      "2296652841/64"
    ],
    [
      "36992809/400",
      "33563048373/8000"
    ],
    [
      "122274841/1296",
      "380322243683/46656"
    ],
    [
      "51607381/529",
      "151517343033/12167"
    ],
    [
      "105077209/225",
      "1073019646052/3375"
    ],
    [
      "186575149/1681",
      "1679597747784/68921"
    ],
    [
      "277758409/2209",
      "3618348227028/103823"
    ],
    [
      "1606748869/1369",
      "64389952137464/50653"
    ],
    [
      "6576877939/53361",
      "408627074635030/12326391"
    ],
    [
      "52592090881/345744",
      "10653722912546335/203297472"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Rank-10 elliptic curve with j-invariant 0, arising from Mestre's polynomial cube-completion construction using the integer sextuple (-111,-9,-1,11,51,59).",
  "created_at": "2026-10-22 08:58:19",
  "updated_at": "2026-10-22 08:58:19"
}