{
  "id": 5669,
  "curve_key": "106830116016:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2225627417",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 76.1835171266721,
  "faltings_height": 4.416866838864165,
  "conductor": "937925188033532192",
  "bad_primes": [
    "2",
    "13",
    "29",
    "233",
    "1949"
  ],
  "discriminant": "705565540590820631911150125632",
  "regulator": "129495.8253106252559134129717856602038002808200737817",
  "points": [
    [
      "-6757",
      "3837976"
    ],
    [
      "-17541",
      "5800224"
    ],
    [
      "790569/16",
      "208973739/64"
    ],
    [
      "-13572",
      "5263674"
    ],
    [
      "6612957/49",
      "15932817732/343"
    ],
    [
      "-351364/49",
      "1354332538/343"
    ],
    [
      "-21853",
      "6180668"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Rank 7, proved: 7 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 04:20:13",
  "updated_at": "2026-10-24 04:20:13"
}