{
  "id": 5574,
  "curve_key": "0:12199521538643491080",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-14119816595652189"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 87.89585681343802,
  "faltings_height": 5.38231064357813,
  "conductor": "1757704149799537651459229058603075",
  "bad_primes": [
    "3",
    "5",
    "7",
    "44267",
    "5207662997"
  ],
  "discriminant": "-86127503340177344921502223871550675",
  "regulator": "182088979359.938976738665502766879649052591375318439342561767",
  "points": [
    [
      "262311",
      "62681993"
    ],
    [
      "455799",
      "283855014"
    ],
    [
      "9629001",
      "29879162028"
    ],
    [
      "2284639/9",
      "1277301491/27"
    ],
    [
      "32403009/64",
      "174127182751/512"
    ],
    [
      "15127809/25",
      "56933172252/125"
    ],
    [
      "17367231/25",
      "70835686254/125"
    ],
    [
      "40253899/81",
      "240255317746/729"
    ],
    [
      "562668891/289",
      "13334093900802/4913"
    ],
    [
      "2185717419/9025",
      "7911869246803/857375"
    ],
    [
      "4148506341/17161",
      "5991864933016/2248091"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization at t = 211/374 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 11 (ellrank bounds [11,11]), with 11 independent rational points.",
  "created_at": "2026-10-23 18:07:02",
  "updated_at": "2026-10-23 18:07:02"
}