{
  "id": 6293,
  "curve_key": "22185687216:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-462201817",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 71.46813959371,
  "faltings_height": 4.023918711117323,
  "conductor": "6836176628419247648",
  "bad_primes": [
    "2",
    "7",
    "11",
    "37",
    "53",
    "3061"
  ],
  "discriminant": "6319386517976620201357152832",
  "regulator": "100817.4285361726538268975748636693491034339443700864",
  "points": [
    [
      "-16324",
      "1787478"
    ],
    [
      "-9317",
      "1870176"
    ],
    [
      "-371",
      "414036"
    ],
    [
      "21571",
      "258852"
    ],
    [
      "28037",
      "3013368"
    ],
    [
      "37312",
      "5890632"
    ],
    [
      "40700",
      "6971910"
    ]
  ],
  "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 23:48:46",
  "updated_at": "2026-10-31 23:48:46"
}