{
  "id": 753,
  "curve_key": "34966208418498164721:-206898331926550229703407151945",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-728462675385378432",
    "239465662134141397669732515"
  ],
  "rank_lower_bound": 14,
  "torsion": [],
  "naive_height": 135.00405006667518,
  "faltings_height": 9.008483315508025,
  "conductor": "512298767178892797693771663917176742",
  "bad_primes": [
    "2",
    "7",
    "11",
    "13",
    "197",
    "19232441",
    "179326747",
    "376628804950709"
  ],
  "discriminant": "-32398123924122419285635681809128533642016068097036288",
  "regulator": "11095273810.2811108809858117480720166574922396427551539113820914934",
  "points": [
    [
      "-972729743",
      "-5259078510155"
    ],
    [
      "-953616803",
      "-8180909750175"
    ],
    [
      "-661401187",
      "-20782854297983"
    ],
    [
      "-24303187",
      "-16036049465983"
    ],
    [
      "409391525",
      "-3139283805391"
    ],
    [
      "421152285",
      "-2715243809055"
    ],
    [
      "434532421",
      "-2230181245839"
    ],
    [
      "446386109",
      "-1799441931295"
    ],
    [
      "449957765",
      "-1669826525815"
    ],
    [
      "452246117",
      "-1586915718935"
    ],
    [
      "476152461",
      "-748708209103"
    ],
    [
      "179662461969/25",
      "-75639037621064763/125"
    ],
    [
      "93452936789/121",
      "-15610757338877485/1331"
    ],
    [
      "1978646685",
      "-80899578120831"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization at T = 98/99 of the rank-11 fibration of X163 described by wgxli for ICARM #718. Independently recovered polynomial sections and rational-point search yield 14 points with an exact independence certificate, proving rank >= 14.",
  "created_at": "2026-09-18 01:07:31",
  "updated_at": "2026-09-18 01:07:31"
}