{
  "id": 6279,
  "curve_key": "-200982432:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "4187134",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 57.35618417765524,
  "faltings_height": 2.847922426446093,
  "conductor": "1122053832573184",
  "bad_primes": [
    "2",
    "7",
    "17",
    "73",
    "241"
  ],
  "discriminant": "-4698189752197486214656",
  "regulator": "13906.450692708505366463691876317197647733342103100",
  "points": [
    [
      "242",
      "32054"
    ],
    [
      "2975",
      "196945"
    ],
    [
      "4088",
      "292292"
    ],
    [
      "8568",
      "815388"
    ],
    [
      "511/9",
      "416465/27"
    ],
    [
      "1241/4",
      "291635/8"
    ]
  ],
  "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 23:39:31",
  "updated_at": "2026-10-31 23:39:31"
}