{
  "id": 755,
  "curve_key": "316815774160491783752537536:-5735478555431090641861659490595799474784",
  "ainvs": [
    "0",
    "1",
    "0",
    "-6600328628343578828177865",
    "6638285365080080725945250624876486400"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 183.0949796371623,
  "faltings_height": 13.145852451826169,
  "conductor": "26659116102684463027381808015526996103613420424556860",
  "bad_primes": [
    "2",
    "3",
    "5",
    "89",
    "131",
    "487",
    "446969",
    "1302233",
    "40737673453",
    "3300212536077131170697"
  ],
  "discriminant": "-634379051551098740963024306612601755354974329742296970970539374600780750000",
  "regulator": "790998792615258.678786386836010201264547967106504102035749075850217746225",
  "points": [
    [
      "-2831987151655",
      "-1617827558075970075"
    ],
    [
      "-2584906219227",
      "-2535319345744942899"
    ],
    [
      "-2206761559360",
      "-3233752768363594920"
    ],
    [
      "-1930569864441",
      "-3490738312411986435"
    ],
    [
      "-1548569888067",
      "-3625710765448651491"
    ],
    [
      "-991683897360",
      "-3494061589818594420"
    ],
    [
      "-652001555635",
      "-3265660745781476355"
    ],
    [
      "-263386787316",
      "-2891098907259668010"
    ],
    [
      "388309328625",
      "-2033191351746150795"
    ],
    [
      "506060990445",
      "-1851409622707508925"
    ],
    [
      "658295042775",
      "-1605800566981772355"
    ],
    [
      "41086411377261/25",
      "-59925075730554082809/125"
    ],
    [
      "1201587635250345/16",
      "-41627689693903321258275/64"
    ],
    [
      "3984075292620",
      "-6601570443213838650"
    ],
    [
      "2154295109415",
      "-1554762418806936195"
    ],
    [
      "22894630360497285/3721",
      "-3201605278416107003328015/226981"
    ],
    [
      "858250243397745/256",
      "-19295323179016885632375/4096"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization at T = -131/356 of the rank-11 fibration of X163 described by wgxli for ICARM #718. Independently recovered polynomial sections and rational-point search yield 17 points with an exact independence certificate, proving rank >= 17.",
  "created_at": "2026-09-18 01:24:04",
  "updated_at": "2026-09-18 01:24:04"
}