{
  "id": 6298,
  "curve_key": "-1257455585712:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "26196991369",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 83.58033425634972,
  "faltings_height": 5.033268266337299,
  "conductor": "43922070834397471626304",
  "bad_primes": [
    "2",
    "41",
    "241",
    "617",
    "4297"
  ],
  "discriminant": "-1150626110557317192509708281370176",
  "regulator": "14985205.9917497732820801397587087979917882039089268228",
  "points": [
    [
      "496100",
      "367551470"
    ],
    [
      "7286153/16",
      "20872746587/64"
    ],
    [
      "9320193/64",
      "42540467583/512"
    ],
    [
      "24386308/729",
      "594989335738/19683"
    ],
    [
      "42458657/1024",
      "1114836956849/32768"
    ],
    [
      "169834628/22201",
      "46880895961178/3307949"
    ],
    [
      "219476772/529",
      "3490156207806/12167"
    ],
    [
      "3913243524/1225",
      "245110573576518/42875"
    ]
  ],
  "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 23:52:12",
  "updated_at": "2026-10-31 23:52:12"
}