{
  "id": 5850,
  "curve_key": "0:377807644016269084800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-437277365759570700"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 94.76183372345217,
  "faltings_height": 5.954475386079309,
  "conductor": "35419466626525226700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "29",
    "37"
  ],
  "discriminant": "-82603365669631889581546936064947680000",
  "regulator": "742296.15063674334140667109439475523913463614521713",
  "points": [
    [
      "1033669",
      "816803897"
    ],
    [
      "29720509",
      "162024521477"
    ],
    [
      "93478021",
      "903782958169"
    ],
    [
      "3255889/4",
      "2555253337/8"
    ],
    [
      "3659929/4",
      "4586860733/8"
    ],
    [
      "58124521/16",
      "441112545419/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(4,-1,-7,3) and specialization t=424/55. On the b=-1, c=-a-d plane, the genus-one square condition has w=13992993/3025, yielding K=185547087180 and, after rational cubic scaling, the cubesum curve u^3+v^3=6872114340. PARI/GP 2.17.4 rank bounds [6,6].",
  "created_at": "2026-10-25 12:01:54",
  "updated_at": "2026-10-25 12:01:54"
}