{
  "id": 5841,
  "curve_key": "0:1907252064117792",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2207467666803"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 70.36887978229291,
  "faltings_height": 3.9217292243160378,
  "conductor": "715219524044172",
  "bad_primes": [
    "2",
    "3",
    "7",
    "31",
    "59",
    "67"
  ],
  "discriminant": "-2105098631991654031400029488",
  "regulator": "8057.09809313981616579530992103564851871704113386",
  "points": [
    [
      "14539",
      "930496"
    ],
    [
      "34699",
      "6290536"
    ],
    [
      "39463",
      "7697362"
    ],
    [
      "2569249/196",
      "581815471/2744"
    ],
    [
      "3503899/225",
      "4227766732/3375"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(5,-2,-1,-3) and specialization t=15/13. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=15440418. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:05:34",
  "updated_at": "2026-10-25 11:05:34"
}