{
  "id": 6278,
  "curve_key": "-104378784:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "2174558",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 55.39061098311106,
  "faltings_height": 2.6841246602340787,
  "conductor": "302636959703296",
  "bad_primes": [
    "2",
    "23",
    "41",
    "1153"
  ],
  "discriminant": "-658101621818479943168",
  "regulator": "13201.242266523851198247394522462606519102359705330",
  "points": [
    [
      "722",
      "44118"
    ],
    [
      "736",
      "44712"
    ],
    [
      "943",
      "53751"
    ],
    [
      "2738",
      "162726"
    ],
    [
      "7544",
      "667644"
    ],
    [
      "9016",
      "867468"
    ]
  ],
  "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 23:38:51",
  "updated_at": "2026-10-31 23:38:51"
}