{
  "id": 5843,
  "curve_key": "0:786119933095200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-909861033675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 68.59626096670543,
  "faltings_height": 3.7740109896837475,
  "conductor": "294794974910700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "31"
  ],
  "discriminant": "-357629947459260257090430000",
  "regulator": "14320.4764422403334543800623053222977821648067847",
  "points": [
    [
      "46531",
      "9991796"
    ],
    [
      "64201/4",
      "14366299/8"
    ],
    [
      "276241/16",
      "131730439/64"
    ],
    [
      "318649/16",
      "169197907/64"
    ],
    [
      "346921/4",
      "204193931/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-5,-16,-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=9912870. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:06:02",
  "updated_at": "2026-10-25 11:06:02"
}