{
  "id": 5594,
  "curve_key": "0:450743625954369757800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-521694011521261294"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 95.11486078979743,
  "faltings_height": 5.983894308274748,
  "conductor": "131659388254401650311201474884075",
  "bad_primes": [
    "3",
    "5",
    "7",
    "63092246291309"
  ],
  "discriminant": "-117575125195887033769160697108351076875",
  "regulator": "1471397397895.85944939922347928621226750808182419741998392445",
  "points": [
    [
      "832776",
      "236324686"
    ],
    [
      "1371454",
      "1434522470"
    ],
    [
      "2521036",
      "3937138446"
    ],
    [
      "3087924",
      "5377965169"
    ],
    [
      "13816761/4",
      "51032059655/8"
    ],
    [
      "160954809/4",
      "2041992754673/8"
    ],
    [
      "69690516/25",
      "574734025814/125"
    ],
    [
      "334298281/324",
      "4428955257913/5832"
    ],
    [
      "9333162636/10609",
      "435961576209415/1092727"
    ],
    [
      "22967096964/625",
      "3480622096632313/15625"
    ],
    [
      "1128383910574/383161",
      "1186325572334271890/237176659"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = 67/404 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with affine parameters (a,b,c,d) = (-13/5,56/5,-2,-32/5) and generating parameters (u,v,w) = (-2,6,-4).\r\n\r\nFound using a sixth-power-residue Mestre–Nagao sieve across Burkhardt surface parameters, with 3-isogeny deduplication and conductor-aware candidate selection.\r\n\r\nPARI/GP 2.17.4 establishes exact rank 11, with bounds [11,11] and 11 independent rational points.",
  "created_at": "2026-10-23 21:30:22",
  "updated_at": "2026-10-23 21:30:22"
}