{
  "id": 5670,
  "curve_key": "9052265136:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-188588857",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 68.77884256383399,
  "faltings_height": 3.799810625294323,
  "conductor": "1138104223506126368",
  "bad_primes": [
    "2",
    "73",
    "109",
    "137",
    "173"
  ],
  "discriminant": "429267549315785808477362752",
  "regulator": "121273.5662152030865262602076768471977034862161183862",
  "points": [
    [
      "-12629",
      "606192"
    ],
    [
      "1730173/9",
      "2269986976/27"
    ],
    [
      "-173",
      "180612"
    ],
    [
      "-1730173/169",
      "2034683448/2197"
    ],
    [
      "113661",
      "38038548"
    ],
    [
      "62453",
      "15225384"
    ],
    [
      "14013",
      "330084"
    ]
  ],
  "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 04:20:40",
  "updated_at": "2026-10-24 04:20:40"
}