{
  "id": 5817,
  "curve_key": "0:811087022852446492800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-938758128301442700"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 96.2898140507979,
  "faltings_height": 6.081807080024786,
  "conductor": "312919376100480900",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "103",
    "463"
  ],
  "discriminant": "-380707267731276075952348325397581280000",
  "regulator": "156841.787469175225035887652987669693732565847305",
  "points": [
    [
      "1001469",
      "256232997"
    ],
    [
      "3631269",
      "6851537847"
    ],
    [
      "134530669",
      "1560385367603"
    ],
    [
      "8544008929/8464",
      "233436763358767/778688"
    ],
    [
      "1393314681721/232324",
      "1641068594034337331/111980168"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-18,-4,-1,22) and specialization t=1/22. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=372927980. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:00:22",
  "updated_at": "2026-10-25 11:00:22"
}