{
  "id": 4690,
  "curve_key": "11933829052896:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-248621438602",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 90.33119478164933,
  "faltings_height": 5.595839976778934,
  "conductor": "3956007662881795565721856",
  "bad_primes": [
    "2",
    "17",
    "101",
    "229",
    "409",
    "773"
  ],
  "discriminant": "983548316266207850626632277313485312",
  "regulator": "552244464.20081217659829337478907769392893950023801125089",
  "points": [
    [
      "-363609",
      "205736967"
    ],
    [
      "-729",
      "13462713"
    ],
    [
      "-17",
      "2055861"
    ],
    [
      "-17491098089/182329",
      "11798946038483073/77854483"
    ],
    [
      "-160815937/6889",
      "43512450521901/571787"
    ],
    [
      "-13399249/49",
      "74785354293/343"
    ],
    [
      "-3969704/9",
      "4169707028/27"
    ],
    [
      "43393673/16",
      "280978426971/64"
    ],
    [
      "85137849/64",
      "728297539629/512"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 - 248621438602 x, rank exactly 9 (PARI ellrank 2-descent: lower = upper = 9). Found by a Mestre-Nagao sieve over all |a| <= 10^12 (a_p via quartic residue classes for p = 1 mod 4), top candidates certified with ellrank.",
  "created_at": "2026-10-20 20:44:58",
  "updated_at": "2026-10-20 20:44:58"
}