{
  "id": 6273,
  "curve_key": "-20797824:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "433288",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 50.55107677144308,
  "faltings_height": 2.2808301425950805,
  "conductor": "750953963776",
  "bad_primes": [
    "2",
    "41",
    "1321"
  ],
  "discriminant": "-5206069456905207808",
  "regulator": "3536.30384991839678997860919253951947545529877711",
  "points": [
    [
      "41",
      "4223"
    ],
    [
      "2952",
      "164328"
    ],
    [
      "6929",
      "579371"
    ],
    [
      "1321/36",
      "862613/216"
    ],
    [
      "5248/9",
      "573344/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 5. 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 23:34:55",
  "updated_at": "2026-10-31 23:34:55"
}