{
  "id": 6291,
  "curve_key": "17672290848:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-368172726",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 70.78579128316393,
  "faltings_height": 3.967056351905151,
  "conductor": "8675273994897348864",
  "bad_primes": [
    "2",
    "3",
    "73",
    "673",
    "1249"
  ],
  "discriminant": "3193999275498267021431883264",
  "regulator": "232768.1801136081166728541544257120410197264998680114",
  "points": [
    [
      "-16152",
      "1316388"
    ],
    [
      "-3650",
      "1138070"
    ],
    [
      "-1752",
      "799788"
    ],
    [
      "26499",
      "2975115"
    ],
    [
      "50475",
      "10488705"
    ],
    [
      "-162866/9",
      "23171390/27"
    ],
    [
      "81433/4",
      "7765747/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 7. 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 23:47:31",
  "updated_at": "2026-10-31 23:47:31"
}