{
  "id": 5730,
  "curve_key": "0:-91121125582944",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "105464265721"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 64.28642157549035,
  "faltings_height": 3.4148577070824913,
  "conductor": "1201252825159527130182828",
  "bad_primes": [
    "2",
    "3",
    "223",
    "472933927"
  ],
  "discriminant": "-4805011300638108520731312",
  "regulator": "720180075655.69187331172186182141543233684929834315173568",
  "points": [
    [
      "-7588611844325/2192206041",
      "25963145197537280554/102641279045661"
    ],
    [
      "-85251388137/30217009",
      "47855901990130484/166102898473"
    ],
    [
      "1107652939335/241149841",
      "1684626788604042104/3744815880889"
    ],
    [
      "2581223882823/405498769",
      "4922386015079692184/8165528711353"
    ],
    [
      "5616563324055/668170801",
      "14444360485507495364/17271547035049"
    ],
    [
      "16123106275179/1335244681",
      "66650888458486653610/48791175888421"
    ],
    [
      "-3576522997119/2568259684",
      "41723248701415389665/130154264265752"
    ],
    [
      "48823838018145/12441617764",
      "565240487581705101007/1387762928632088"
    ],
    [
      "-1121102658492081/546069271225",
      "125554818438452017565428/403526079010782125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed from a rank-four Mordell family obtained through a rational parametrization of the Burkhardt quartic.\r\n\r\nThe construction parameters are (u,v,w) = (-1,2,2), with specialization t = -155/199.\r\n\r\nPARI/GP 2.17.4 computation returned matching rank bounds [9,9] and nine rational points on the original curve.",
  "created_at": "2026-10-24 17:17:39",
  "updated_at": "2026-10-24 17:17:39"
}