{
  "id": 5591,
  "curve_key": "0:45497070695644776",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-52658646638478"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 76.71284867695918,
  "faltings_height": 4.45039329887156,
  "conductor": "2362735866713806045837778481",
  "bad_primes": [
    "3",
    "13",
    "1367",
    "2843",
    "320699"
  ],
  "discriminant": "-1197907084423899665239753689867",
  "regulator": "34122641193.39840290443630434003517716510156862111651954537",
  "points": [
    [
      "47840",
      "7538641"
    ],
    [
      "383162",
      "237066550"
    ],
    [
      "365950/9",
      "103051682/27"
    ],
    [
      "8922394/225",
      "10511372647/3375"
    ],
    [
      "117492128/529",
      "1270477454903/12167"
    ],
    [
      "485216329/9216",
      "8545049892037/884736"
    ],
    [
      "313639664/1681",
      "5531957045897/68921"
    ],
    [
      "1148839224/19321",
      "33711586832163/2685619"
    ],
    [
      "4914669890/121801",
      "153479258527534/42508549"
    ],
    [
      "8838386388/27889",
      "830232864807207/4657463"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = -31/409 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with affine parameters (a,b,c,d) = (11/5,74/5,-8,26) and generating parameters (u,v,w) = (4,6,-4).\r\n\r\nFound using a sixth-power-residue Mestre–Nagao sieve across Burkhardt surface parameters, 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 21:28:10",
  "updated_at": "2026-10-23 21:28:10"
}