{
  "id": 6286,
  "curve_key": "12151680096:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-253160002",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 69.66219983003823,
  "faltings_height": 3.8734237308113433,
  "conductor": "4101759143208960256",
  "bad_primes": [
    "2",
    "113",
    "593",
    "1889"
  ],
  "discriminant": "1038401352898298664826880512",
  "regulator": "283725.5865569870415595024506814369109805936199770363",
  "points": [
    [
      "-15488",
      "453552"
    ],
    [
      "-4744",
      "1046052"
    ],
    [
      "-2825",
      "832245"
    ],
    [
      "58114",
      "13474146"
    ],
    [
      "-603081/121",
      "1419853701/1331"
    ],
    [
      "67009/4",
      "5427729/8"
    ],
    [
      "569873/16",
      "384884871/64"
    ]
  ],
  "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 23:43:48",
  "updated_at": "2026-10-31 23:43:48"
}