{
  "id": 5673,
  "curve_key": "1320058675296:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-27501222402",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 83.72609190756219,
  "faltings_height": 5.045414737271673,
  "conductor": "5378255883408118397184",
  "bad_primes": [
    "2",
    "3",
    "19",
    "41",
    "67",
    "73",
    "401"
  ],
  "discriminant": "1331177500660244811959744590643712",
  "regulator": "980655.058406497618368442525299518334840424746504378223",
  "points": [
    [
      "-52193",
      "35960977"
    ],
    [
      "-26937",
      "26856189"
    ],
    [
      "-91656",
      "41840964"
    ],
    [
      "-6690888/121",
      "48933809388/1331"
    ],
    [
      "-142721",
      "31904191"
    ],
    [
      "-162729",
      "12886587"
    ],
    [
      "213282",
      "61939602"
    ],
    [
      "8455266/49",
      "6795215442/343"
    ]
  ],
  "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 04:21:13",
  "updated_at": "2026-10-24 04:21:13"
}