{
  "id": 6306,
  "curve_key": "-28113048292800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "585688506100",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 92.9017648096414,
  "faltings_height": 5.810054145778274,
  "conductor": "27442482094211978976800",
  "bad_primes": [
    "2",
    "5",
    "101",
    "181",
    "421",
    "761"
  ],
  "discriminant": "-12858197073148010738917278846784000000",
  "regulator": "58407026.1827057464919211563579603763746407485242283471",
  "points": [
    [
      "412580",
      "558456500"
    ],
    [
      "1472580",
      "2013889500"
    ],
    [
      "2203856",
      "3463359704"
    ],
    [
      "1640745/4",
      "4448865675/8"
    ],
    [
      "12480545/16",
      "61768162225/64"
    ],
    [
      "46101605/49729",
      "258405300636175/11089567"
    ],
    [
      "2588678480/44521",
      "1738549995471800/9393931"
    ],
    [
      "5788565525/49",
      "440418490064825/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8. 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 23:56:54",
  "updated_at": "2026-10-31 23:56:54"
}