{
  "id": 5808,
  "curve_key": "0:108267981158526708097152",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-125310163377924430668"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 106.07779282732643,
  "faltings_height": 6.897471978068832,
  "conductor": "41770054459308143556",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "23",
    "31",
    "37",
    "307"
  ],
  "discriminant": "-6783539203786512885208747083532197616128768",
  "regulator": "26349.6998200195361254497082683028414896880109864",
  "points": [
    [
      "7394709",
      "16704647631"
    ],
    [
      "20071353/4",
      "8128897965/8"
    ],
    [
      "33930561/4",
      "176192583777/8"
    ],
    [
      "327913761/64",
      "1552552105167/512"
    ],
    [
      "1147218323421/21025",
      "1228291791394074219/3048625"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-5,-13,-1,18) and specialization t=1/18. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=4308650444. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:58:21",
  "updated_at": "2026-10-25 10:58:21"
}