{
  "id": 5812,
  "curve_key": "0:11915970584060743200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-13791632620440675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 87.84882248026456,
  "faltings_height": 5.378391115813676,
  "conductor": "4468488969022778700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "31"
  ],
  "discriminant": "-82170344305671834157847076004830000",
  "regulator": "42936.9669693206778357654217852393336868081854126",
  "points": [
    [
      "240331",
      "9468004"
    ],
    [
      "261079",
      "63277942"
    ],
    [
      "1039129/4",
      "489260317/8"
    ],
    [
      "4441801/4",
      "9314090149/8"
    ],
    [
      "43157569/4",
      "283519592447/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-16,-5,-1,21) and specialization t=10/1. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=1220449230. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:59:14",
  "updated_at": "2026-10-25 10:59:14"
}