{
  "id": 5835,
  "curve_key": "0:9428300019740448",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-10912384282107"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 73.56498440336475,
  "faltings_height": 4.188071276072025,
  "conductor": "3535612507402668",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "31",
    "47"
  ],
  "discriminant": "-51442616471202391288475281968",
  "regulator": "31455.9774658400561213811116046219126289334038867",
  "points": [
    [
      "32767",
      "4926334"
    ],
    [
      "88753/4",
      "850423/8"
    ],
    [
      "390817/16",
      "122455921/64"
    ],
    [
      "531433/4",
      "386509333/8"
    ],
    [
      "718921/16",
      "571730117/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(23,-14,-9,-1) and specialization t=-2/19. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=34329834. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:04:11",
  "updated_at": "2026-10-25 11:04:11"
}