{
  "id": 5671,
  "curve_key": "6960967968:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-145020166",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 67.99075313245397,
  "faltings_height": 3.734136506012655,
  "conductor": "1345974306986723584",
  "bad_primes": [
    "2",
    "17",
    "43",
    "281",
    "353"
  ],
  "discriminant": "195193417430949613947794944",
  "regulator": "167546.6524779694842429260543753528372438008766620532",
  "points": [
    [
      "-12002",
      "108018"
    ],
    [
      "-9554",
      "716550"
    ],
    [
      "205411/9",
      "79083235/27"
    ],
    [
      "258043/9",
      "118957823/27"
    ],
    [
      "-5746",
      "802230"
    ],
    [
      "234073/16",
      "64303197/64"
    ],
    [
      "-4802",
      "765282"
    ]
  ],
  "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 04:20:51",
  "updated_at": "2026-10-24 04:20:51"
}