{
  "id": 5590,
  "curve_key": "0:17562015726717096",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-20326407091108"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 74.80902953469004,
  "faltings_height": 4.291741703682465,
  "conductor": "244837229767961732153553843",
  "bad_primes": [
    "3",
    "283",
    "10640705191"
  ],
  "discriminant": "-178486340500844102739940751547",
  "regulator": "213623646.9386728417571897896031218446502518865636413635647",
  "points": [
    [
      "113241/4",
      "12298721/8"
    ],
    [
      "30342",
      "2758180"
    ],
    [
      "35902",
      "5094075"
    ],
    [
      "36732",
      "5406835"
    ],
    [
      "39954",
      "6591892"
    ],
    [
      "174441/4",
      "63303161/8"
    ],
    [
      "210873/4",
      "89867057/8"
    ],
    [
      "60420",
      "14150668"
    ],
    [
      "64002",
      "15551275"
    ],
    [
      "64920",
      "15914956"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = -208/211 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, using affine parameters (a,b,c,d) = (2,12,-4,7).\r\n\r\nFound by a sixth-power-residue Mestre–Nagao sieve, with 3-isogeny deduplication and conductor-aware candidate selection.\r\n\r\nPARI/GP 2.17.4 establishes exact rank 10, with bounds [10,10] and 10 independent rational points.",
  "created_at": "2026-10-23 21:22:47",
  "updated_at": "2026-10-23 21:22:47"
}