{
  "id": 5803,
  "curve_key": "0:11995809359688",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-13884038611"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 60.23115696939807,
  "faltings_height": 3.0769189899081346,
  "conductor": "18512051481",
  "bad_primes": [
    "3",
    "7",
    "11",
    "19",
    "31"
  ],
  "discriminant": "-83275140158552213286723",
  "regulator": "119.7943915878311603715459275448069081162756376",
  "points": [
    [
      "2451",
      "28984"
    ],
    [
      "2821",
      "92550"
    ],
    [
      "12369/4",
      "1001885/8"
    ],
    [
      "4123",
      "237072"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-5,-3,-1,8) and specialization t=17/3. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=45353. PARI/GP 2.17.4 returned matching computational rank bounds [4,4].",
  "created_at": "2026-10-25 10:57:13",
  "updated_at": "2026-10-25 10:57:13"
}