{
  "id": 5908,
  "curve_key": "0:481652649421171488",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-557468344237467"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 81.43199920963582,
  "faltings_height": 4.84365584326128,
  "conductor": "180619743532939308",
  "bad_primes": [
    "2",
    "3",
    "13",
    "19",
    "229",
    "241"
  ],
  "discriminant": "-134253052485204818827736600870448",
  "regulator": "42026.811741193263894837351171441179438208579855938",
  "points": [
    [
      "92287",
      "15117206"
    ],
    [
      "435487",
      "286412594"
    ],
    [
      "416689/4",
      "191498359/8"
    ],
    [
      "13631683/49",
      "49673852852/343"
    ],
    [
      "18722353/64",
      "80103332777/512"
    ],
    [
      "259001977/36",
      "4168255132691/216"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic specialization b = -1, c = -a - d with (a,d) = (3,12), using the auxiliary quartic rational point t = 16179/2645, w = 25201350720/279841. The resulting cubesum curve is u^3 + v^3 = 245370294 after rational cube scaling. PARI/GP 2.17.4 ellrank bounds [6,6].",
  "created_at": "2026-10-25 21:06:56",
  "updated_at": "2026-10-25 21:06:56"
}