{
  "id": 5834,
  "curve_key": "0:9920512309590792",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-11482074432397"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 73.66676191797185,
  "faltings_height": 4.196552735622617,
  "conductor": "3720192116096547",
  "bad_primes": [
    "3",
    "7",
    "13",
    "19",
    "31",
    "73"
  ],
  "discriminant": "-56954030373114832232330145363",
  "regulator": "1260.74832695017990891227949818346262368382215100",
  "points": [
    [
      "126217/4",
      "35719407/8"
    ],
    [
      "145483",
      "55386909"
    ],
    [
      "205933",
      "93390615"
    ],
    [
      "300979",
      "165086981"
    ],
    [
      "3912727/121",
      "6289707987/1331"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-8,-7,-1,15) and specialization t=7/1. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=35214543. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:04:00",
  "updated_at": "2026-10-25 11:04:00"
}