{
  "id": 6280,
  "curve_key": "292635696:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-6096577",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 58.483317105024724,
  "faltings_height": 2.941850170393551,
  "conductor": "1189384035741728",
  "bad_primes": [
    "2",
    "41",
    "241",
    "617"
  ],
  "discriminant": "14502342712940393730112",
  "regulator": "15807.039659536792777230640182190741449122763435694",
  "points": [
    [
      "-2468",
      "3702"
    ],
    [
      "-2401",
      "28224"
    ],
    [
      "-2169",
      "54948"
    ],
    [
      "-148697/121",
      "99924384/1331"
    ],
    [
      "88929/25",
      "19090092/125"
    ],
    [
      "1338273/289",
      "1309723176/4913"
    ]
  ],
  "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 23:40:07",
  "updated_at": "2026-10-31 23:40:07"
}