{
  "id": 6294,
  "curve_key": "-48606720384:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1012640008",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 73.8210829133979,
  "faltings_height": 4.219997321091316,
  "conductor": "4101759143208960256",
  "bad_primes": [
    "2",
    "113",
    "593",
    "1889"
  ],
  "discriminant": "-66457686585491114548920352768",
  "regulator": "567451.1731139740831190049013628738219611872399540727",
  "points": [
    [
      "200",
      "450040"
    ],
    [
      "593",
      "775051"
    ],
    [
      "1889/4",
      "5532881/8"
    ],
    [
      "177184/9",
      "141759856/27"
    ],
    [
      "241792/9",
      "184305952/27"
    ],
    [
      "4172801/16",
      "8587180543/64"
    ],
    [
      "8577152/121",
      "27534802208/1331"
    ]
  ],
  "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 23:49:31",
  "updated_at": "2026-10-31 23:49:31"
}