{
  "id": 5729,
  "curve_key": "0:-35808565956984",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "41445099487"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 62.41841650651109,
  "faltings_height": 3.2591906180008863,
  "conductor": "247348263097159230659409",
  "bad_primes": [
    "3",
    "281",
    "589965829"
  ],
  "discriminant": "-742044789291477691978227",
  "regulator": "572914469533.95997800082303306365147729885001002288327432",
  "points": [
    [
      "-41187833927/12124324",
      "1998381322182785/42216896168"
    ],
    [
      "-40522914431/12503296",
      "3803734524905537/44211654656"
    ],
    [
      "-3066622064495/1131380496",
      "5584012880956261543/38055114363456"
    ],
    [
      "-3011615338607/1160628624",
      "6122225680774859033/39540295962432"
    ],
    [
      "-1755391350383/1222621156",
      "8386578412666491955/42750171340696"
    ],
    [
      "13618104193/34951744",
      "42096741902026817/206634710528"
    ],
    [
      "163032053185/75411856",
      "148685868058681409/654876557504"
    ],
    [
      "42946133712913/11791353744",
      "383606742888107252263/1280399520353472"
    ],
    [
      "763190704269505/17372294416",
      "21088986244086321784319/2289737893206464"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "This curve is the 3-isogenous partner of the Mordell curve obtained from the Burkhardt rank-four family with parameters (u,v,w) = (-5,4,-2) and specialization t = -141/74.\r\n\r\nThe original curve has archived matching PARI/GP rank bounds [9,9]. ",
  "created_at": "2026-10-24 17:01:19",
  "updated_at": "2026-10-24 17:01:19"
}