{
  "id": 6289,
  "curve_key": "15985802976:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-333037562",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 70.4849005538703,
  "faltings_height": 3.941982124464016,
  "conductor": "7098497132985846016",
  "bad_primes": [
    "2",
    "11",
    "13",
    "23",
    "197",
    "257"
  ],
  "discriminant": "2364066179033595937676052992",
  "regulator": "107043.4625708874811292589528903323017676294209451164",
  "points": [
    [
      "-18216",
      "148764"
    ],
    [
      "-3289",
      "1029457"
    ],
    [
      "21528",
      "1675596"
    ],
    [
      "60138",
      "14052246"
    ],
    [
      "144992",
      "54770728"
    ],
    [
      "-36751/4",
      "12091079/8"
    ],
    [
      "167050/9",
      "12461930/27"
    ]
  ],
  "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 23:46:01",
  "updated_at": "2026-10-31 23:46:01"
}