{
  "id": 5811,
  "curve_key": "0:18633973339182247200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-21567098772201675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 88.74303622431621,
  "faltings_height": 5.45290892781798,
  "conductor": "6987740002193342700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "67",
    "173"
  ],
  "discriminant": "-200940371762358094822250009052030000",
  "regulator": "70465.4767133989601240767279464660103536732038454",
  "points": [
    [
      "360259",
      "158712548"
    ],
    [
      "1842031",
      "2495713954"
    ],
    [
      "2873161/4",
      "4726288741/8"
    ],
    [
      "12428299/25",
      "39783434468/125"
    ],
    [
      "25634401/64",
      "105788735249/512"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-7,-2,9,-1) and specialization t=-17/24. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=1526186970. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:59:02",
  "updated_at": "2026-10-25 10:59:02"
}