{
  "id": 6303,
  "curve_key": "4161944201856:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-86707170872",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 87.17101031172061,
  "faltings_height": 5.332491270951541,
  "conductor": "30072533922504820961536",
  "bad_primes": [
    "2",
    "7",
    "17",
    "31",
    "73",
    "167",
    "241"
  ],
  "discriminant": "41720069397962270677690708665270272",
  "regulator": "572846037.168412003390782031983381018145947676764831305",
  "points": [
    [
      "-1071",
      "9636501"
    ],
    [
      "-4261331868521679/47154556801",
      "862667156964632264582757/10239659163893951"
    ],
    [
      "-4088/9",
      "169443512/27"
    ],
    [
      "-1687/16",
      "193510709/64"
    ],
    [
      "3908529/4",
      "7367948841/8"
    ],
    [
      "10995625/36",
      "9685386325/216"
    ],
    [
      "5943330649/17424",
      "231269342328611/2299968"
    ],
    [
      "59415227936/60025",
      "13826935347088816/14706125"
    ]
  ],
  "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 23:55:05",
  "updated_at": "2026-10-31 23:55:05"
}