{
  "id": 6287,
  "curve_key": "14186834016:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-295559042",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 70.12674056844816,
  "faltings_height": 3.9121354590121697,
  "conductor": "5590729427709296896",
  "bad_primes": [
    "2",
    "17",
    "73",
    "193",
    "617"
  ],
  "discriminant": "1652390633734968045075333632",
  "regulator": "200182.8286662463552693463726105021613795161933804303",
  "points": [
    [
      "-14089",
      "1169387"
    ],
    [
      "-11169",
      "1381233"
    ],
    [
      "28178",
      "3747674"
    ],
    [
      "-1014408/121",
      "1829146692/1331"
    ],
    [
      "-14089/25",
      "50988091/125"
    ],
    [
      "164050/9",
      "22081130/27"
    ],
    [
      "1141209/16",
      "1183180131/64"
    ]
  ],
  "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 23:44:33",
  "updated_at": "2026-10-31 23:44:33"
}