{
  "id": 6310,
  "curve_key": "176183823074016:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3670496314042",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 98.40764704557965,
  "faltings_height": 6.268877665439795,
  "conductor": "862242764249338130328176896",
  "bad_primes": [
    "2",
    "61",
    "97",
    "241",
    "1061",
    "1213"
  ],
  "discriminant": "3164858887986580780407697108581744773632",
  "regulator": "68229979.030080555830217403350449676418155288956369521331",
  "points": [
    [
      "-1893537",
      "401219451"
    ],
    [
      "-1286993",
      "1610028243"
    ],
    [
      "-838953",
      "1577619543"
    ],
    [
      "-175689",
      "799651737"
    ],
    [
      "-42777",
      "396149649"
    ],
    [
      "2289818",
      "1897724274"
    ],
    [
      "17832313/4",
      "67994609469/8"
    ],
    [
      "1729734361/36",
      "71882570840077/216"
    ],
    [
      "37840168186/7921",
      "6743004450240642/704969"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 9. 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 23:59:14",
  "updated_at": "2026-10-31 23:59:14"
}