{
  "id": 6284,
  "curve_key": "-427386384:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "8903883",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 59.619597127792055,
  "faltings_height": 3.0365401722908283,
  "conductor": "2536932239286048",
  "bad_primes": [
    "2",
    "3",
    "73",
    "109",
    "373"
  ],
  "discriminant": "-45177095675061949848768",
  "regulator": "13344.427839360105639026736177474809880484870685333",
  "points": [
    [
      "109",
      "31174"
    ],
    [
      "327",
      "54282"
    ],
    [
      "5341",
      "447118"
    ],
    [
      "73/4",
      "101981/8"
    ],
    [
      "7957/9",
      "2498498/27"
    ],
    [
      "7957/169",
      "44988878/2197"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 6. Rank proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file families/family_Z2.add_2026-10-24.part1.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:42:23",
  "updated_at": "2026-10-31 23:42:23"
}