{
  "id": 5576,
  "curve_key": "0:-3045922934940618264",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "3525373767292382"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 85.12067125526455,
  "faltings_height": 5.151045180397008,
  "conductor": "50101326073522937635710189489",
  "bad_primes": [
    "3",
    "7",
    "10658726431723"
  ],
  "discriminant": "-5369008406016938565855611036209707",
  "regulator": "422747866.7028079263142718337482877559238035635963798210718",
  "points": [
    [
      "-131628",
      "35281669"
    ],
    [
      "-117530",
      "43610738"
    ],
    [
      "-108300",
      "47488261"
    ],
    [
      "-15960",
      "59340613"
    ],
    [
      "3892",
      "59375354"
    ],
    [
      "22974",
      "59476882"
    ],
    [
      "214242",
      "115581154"
    ],
    [
      "2516640",
      "3992819386"
    ],
    [
      "525777/16",
      "3819067591/64"
    ],
    [
      "1267204/25",
      "7557701233/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization at t = -79491/16285 of the generic rank-4 Mordell family associated with the Burkhardt quartic, with parameters (a,b,c,d) = (-43/36,-5/12,1/4,7/9).\r\n\r\nFound using a Mestre–Nagao sieve combined with p-adic coefficient reduction. The specialization satisfies m = 103n (mod 637), guaranteeing a sixth-power factor 637^6 in the integral Mordell coefficient. An additional factor 17^6 produces an especially compact model.\r\n\r\nPARI/GP 2.17.4 verifies exact rank 10, with bounds [10,10] and 10 independent rational points.",
  "created_at": "2026-10-23 18:40:08",
  "updated_at": "2026-10-23 18:40:08"
}