{
  "id": 6292,
  "curve_key": "-18293042064:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "381105043",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 70.88935982823521,
  "faltings_height": 3.975687063994425,
  "conductor": "4647713721601019168",
  "bad_primes": [
    "2",
    "11",
    "113",
    "257",
    "1193"
  ],
  "discriminant": "-3542534275444892877728928448",
  "regulator": "244760.0117534931437737430509163939029693511499163431",
  "points": [
    [
      "2816",
      "1046672"
    ],
    [
      "5819",
      "1553926"
    ],
    [
      "6425",
      "1647370"
    ],
    [
      "92777",
      "28878062"
    ],
    [
      "101772",
      "33058938"
    ],
    [
      "261369",
      "133995174"
    ],
    [
      "2352321/121",
      "5112900378/1331"
    ]
  ],
  "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 23:48:05",
  "updated_at": "2026-10-31 23:48:05"
}