{
  "id": 5709,
  "curve_key": "0:-4496855702833509624",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "5204694100501747"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 85.89982018747592,
  "faltings_height": 5.215974258081289,
  "conductor": "1624653501828766194979144041489",
  "bad_primes": [
    "3",
    "7",
    "60696141113723"
  ],
  "discriminant": "-11702379173672602902434774530845267",
  "regulator": "12436118604.2532182712774679345435574947075014943710989690744",
  "points": [
    [
      "77875",
      "75345658"
    ],
    [
      "93319",
      "77571622"
    ],
    [
      "1140433/4",
      "1347714077/8"
    ],
    [
      "440419",
      "301051957"
    ],
    [
      "8932567",
      "26697218089"
    ],
    [
      "-1288931/25",
      "8898426128/125"
    ],
    [
      "-2753303/16",
      "668225365/64"
    ],
    [
      "288085/9",
      "1954003832/27"
    ],
    [
      "3071425/16",
      "7091768449/64"
    ],
    [
      "8058505/64",
      "43447607717/512"
    ],
    [
      "13602505/36",
      "52532622503/216"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed from the Burkhardt quartic using the rational Bruin–Nasserden parametrization with parameters (u,v,w)=(-1/5,0,6/5), specialized at t=-340/57. Candidates were selected using a three-stage Mestre–Nagao sieve, followed by PARI/GP 2.17.4 rank computations. Eleven rational-point witnesses were verified exactly on the minimal Weierstrass model. PARI returned matching computational rank bounds [11,11].",
  "created_at": "2026-10-24 14:41:56",
  "updated_at": "2026-10-24 14:41:56"
}