{
  "id": 5593,
  "curve_key": "0:20657669274942672290472",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-23909339438591055892"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 102.76474719358443,
  "faltings_height": 6.621384841923664,
  "conductor": "41735582127674531636546296520307",
  "bad_primes": [
    "3",
    "7",
    "11",
    "37",
    "292343",
    "1492747"
  ],
  "discriminant": "-246955613352378768459234899167754471494203",
  "regulator": "1611679925.24381677181131277454706745473247293442453774403182",
  "points": [
    [
      "2896894",
      "633545643"
    ],
    [
      "2924628",
      "1051815964"
    ],
    [
      "2928772",
      "1101273827"
    ],
    [
      "3292674",
      "3433489636"
    ],
    [
      "16777761/4",
      "56503353749/8"
    ],
    [
      "7177038",
      "18595133419"
    ],
    [
      "8393154",
      "23819040283"
    ],
    [
      "13717158",
      "50567943604"
    ],
    [
      "28108234",
      "148941741371"
    ],
    [
      "239751897/4",
      "3712094005847/8"
    ],
    [
      "124803294/25",
      "1253130272447/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = -169/16 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with affine parameters (a,b,c,d) = (-10,-32,-9,-4) and generating parameters (u,v,w) = (3,-2,-6).\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 11, with bounds [11,11] and 11 independent rational points.",
  "created_at": "2026-10-23 21:29:43",
  "updated_at": "2026-10-23 21:29:43"
}