{
  "id": 5871,
  "curve_key": "0:484722418987167769800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-561021318272184919"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 95.26021613800123,
  "faltings_height": 5.996007253958398,
  "conductor": "2244085273088739675",
  "bad_primes": [
    "3",
    "5",
    "7",
    "19",
    "23",
    "61",
    "103"
  ],
  "discriminant": "-135969805248131609764321156557815851875",
  "regulator": "10099949.987748500094500180770355020751822782338296",
  "points": [
    [
      "5008369/4",
      "9472241643/8"
    ],
    [
      "518145961/484",
      "-8689120583433/10648"
    ],
    [
      "3612289/4",
      "-3351128891/8"
    ],
    [
      "3477961/4",
      "-2482899863/8"
    ],
    [
      "3718681/4",
      "3939383767/8"
    ],
    [
      "1002600649/900",
      "24471160843607/27000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, on b=-1, c=-a-d. Specialization (a,b,c,d)=(-46,-1,48,-2), t=-23/29, w=564921/841 on w^2=D_{a,d}(t), where D_{a,d}(t)=L_{a,d}(t)^2-4(a^3+1)d^3(t-a)(t-d)^3 and the cubesum parameter k=(a^3+1)(t-a)w/8 up to rational cubic scaling, yields u^3+v^3=288295455. PARI/GP 2.17.4 ellrank bounds [6,6].",
  "created_at": "2026-10-25 17:51:33",
  "updated_at": "2026-10-25 17:51:33"
}