{
  "id": 5672,
  "curve_key": "-1593474451344:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "33197384403",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 84.29081381289309,
  "faltings_height": 5.092474896049247,
  "conductor": "3918458066490836147232",
  "bad_primes": [
    "2",
    "3",
    "107",
    "241",
    "313",
    "457"
  ],
  "discriminant": "-2341486056605983575417867751604928",
  "regulator": "1282156.94896875965631914366497782495918128802365674341",
  "points": [
    [
      "146697/4",
      "284738877/8"
    ],
    [
      "110137/4",
      "-244614277/8"
    ],
    [
      "8667",
      "16981542"
    ],
    [
      "939",
      "5583294"
    ],
    [
      "75433",
      "54160894"
    ],
    [
      "106061931/289",
      "1219500082638/4913"
    ],
    [
      "2892",
      "9799542"
    ],
    [
      "3696217/4",
      "7243001227/8"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Rank 8, proved: 8 independent points listed, matching the 2-descent upper bound. Torsion Z/2. Member of the family y^2 = x^3 + a x.",
  "created_at": "2026-10-24 04:21:02",
  "updated_at": "2026-10-24 04:21:02"
}