{
  "id": 5532,
  "curve_key": "-763869676597632:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "15913951595784",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 102.80825493052497,
  "faltings_height": 6.635594989185238,
  "conductor": "389471519250989804116224",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "211",
    "433",
    "761"
  ],
  "discriminant": "-257937254154827803026009084602688694419456",
  "regulator": "91569081.2693439738484282805678373610493012542553387386",
  "points": [
    [
      "271848225/4",
      "4489899653745/8"
    ],
    [
      "751393897/64",
      "21753392700491/512"
    ],
    [
      "809759553/49",
      "23704604901027/343"
    ],
    [
      "1356155025/49",
      "50457894632235/343"
    ],
    [
      "3047336224/169",
      "172288771764400/2197"
    ],
    [
      "40556401152/247009",
      "198609051184917696/122763473"
    ],
    [
      "709177878600/2401",
      "597272304232858680/117649"
    ],
    [
      "709177878600/121801",
      "723947358935299320/42508549"
    ]
  ],
  "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": "2026-10-22 22:49:43",
  "updated_at": "2026-10-22 22:49:43"
}