{
  "id": 6282,
  "curve_key": "-316431072:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "6592314",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 58.71784798152013,
  "faltings_height": 2.961394410101501,
  "conductor": "2781350647974144",
  "bad_primes": [
    "2",
    "3",
    "47",
    "97",
    "241"
  ],
  "discriminant": "-18335536815549021129216",
  "regulator": "16369.230631562898502801173830873377584321514555990",
  "points": [
    [
      "94",
      "24910"
    ],
    [
      "1128",
      "94188"
    ],
    [
      "2350",
      "168730"
    ],
    [
      "2619",
      "187695"
    ],
    [
      "5547",
      "455241"
    ],
    [
      "40608",
      "8199432"
    ]
  ],
  "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 23:40:45",
  "updated_at": "2026-10-31 23:40:45"
}