{
  "id": 5575,
  "curve_key": "0:-4633179722704401624",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "5362476530907872"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 85.95955014287725,
  "faltings_height": 5.220951754364733,
  "conductor": "115923021595516162928902260609",
  "bad_primes": [
    "3",
    "7",
    "16213080970243"
  ],
  "discriminant": "-12422658763240298567949952953642267",
  "regulator": "501907394.7623660791030964734334831496415002205320135758013",
  "points": [
    [
      "-112728",
      "62689504"
    ],
    [
      "440601/4",
      "654776321/8"
    ],
    [
      "282660",
      "167170783"
    ],
    [
      "434994",
      "296094487"
    ],
    [
      "611412",
      "483656224"
    ],
    [
      "671622",
      "555261304"
    ],
    [
      "3030601/4",
      "5308284271/8"
    ],
    [
      "-2650746/25",
      "8072381867/125"
    ],
    [
      "1212225/16",
      "4872992449/64"
    ],
    [
      "16935468/49",
      "74082068320/343"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization at t = 501/565 of the rank-4 Mordell family associated with the Burkhardt quartic, using parameters (a,b,c,d) = (-43/36,-5/12,1/4,7/9).\r\n\r\nFound using a sixth-power-residue Mestre–Nagao sieve over rational specializations. PARI/GP 2.17.4 gives exact rank 10 (ellrank bounds [10,10]), with 10 independent rational points.",
  "created_at": "2026-10-23 18:08:10",
  "updated_at": "2026-10-23 18:08:10"
}