{
  "id": 6299,
  "curve_key": "-1629129526032:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "33940198459",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 84.35720086497464,
  "faltings_height": 5.098007150389377,
  "conductor": "36861986285961791189792",
  "bad_primes": [
    "2",
    "29",
    "53",
    "59",
    "241",
    "1553"
  ],
  "discriminant": "-2502206260276959037345316429861056",
  "regulator": "212185982.082331737136995906887463724332021661969759826",
  "points": [
    [
      "76097/4",
      "204363929/8"
    ],
    [
      "2386961/16",
      "5859989255/64"
    ],
    [
      "2877317/49",
      "16071556654/343"
    ],
    [
      "2975625/24964",
      "7933421940675/3944312"
    ],
    [
      "587603951/12769",
      "58775886476890/1442897"
    ],
    [
      "1916900513/6724",
      "99925816977833/551368"
    ],
    [
      "9747984629/87025",
      "1852543300026742/25672375"
    ],
    [
      "46244339948/1329409",
      "53598427538481478/1532808577"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8. 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 23:52:46",
  "updated_at": "2026-10-31 23:52:46"
}