{
  "id": 6295,
  "curve_key": "-68409979584:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1425207908",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 74.84635365385012,
  "faltings_height": 4.305436549462334,
  "conductor": "4062435162051472928",
  "bad_primes": [
    "2",
    "73",
    "89",
    "173",
    "317"
  ],
  "discriminant": "-185274070998176663041072467968",
  "regulator": "357390.4419809387962901888953489700670378513044541824",
  "points": [
    [
      "4325",
      "2498985"
    ],
    [
      "12816",
      "4513368"
    ],
    [
      "22784",
      "6655776"
    ],
    [
      "56052",
      "15999732"
    ],
    [
      "58473/4",
      "39157419/8"
    ],
    [
      "103952/49",
      "597360168/343"
    ],
    [
      "4495924/169",
      "16549496244/2197"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 7. 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 23:50:09",
  "updated_at": "2026-10-31 23:50:09"
}