{
  "id": 5832,
  "curve_key": "0:19712711162944800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-22815637920075"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 75.04008011855328,
  "faltings_height": 4.310995919004402,
  "conductor": "7392266686104300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29"
  ],
  "discriminant": "-224879040158384565542018430000",
  "regulator": "20284.7986838920590929026992547982165479859000831",
  "points": [
    [
      "32851",
      "3554824"
    ],
    [
      "136591",
      "50255114"
    ],
    [
      "707161/4",
      "593442941/8"
    ],
    [
      "2159521/4",
      "3173252719/8"
    ],
    [
      "5240599/121",
      "10173882082/1331"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-7,-3,-1,10) and specialization t=-6/17. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=49639590. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:03:32",
  "updated_at": "2026-10-25 11:03:32"
}