{
  "id": 6033,
  "curve_key": "34146564489354003611165804021641:-191799497042724616369394095128746001397975489189",
  "ainvs": [
    "1",
    "0",
    "1",
    "-711386760194875075232620917118",
    "221990158614264542997161297566829380381098908"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 217.82464431051906,
  "faltings_height": 16.079228662157288,
  "conductor": "101164411429739150871932825580925108907114527197963443603225211803566536418110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "13317956467",
    "135981212614783",
    "13226906932995318982937522899361934859799666221"
  ],
  "discriminant": "1751986579203881860685957837715627579477435566986429832485519444642983239939944370900062500",
  "regulator": "29354168927690873506652.10044386869012860099435843994809686283635608640820391325164",
  "points": [
    [
      "565363806355219",
      "713154483832540064015"
    ],
    [
      "-509643659831396",
      "21264307641557153887700"
    ],
    [
      "316993292046484",
      "5323374560417789885255"
    ],
    [
      "4799351924389894",
      "327650735129897642700665"
    ],
    [
      "-493269620455796",
      "21280878478761423285620"
    ],
    [
      "-864127418933831",
      "-13836943750347764605285"
    ],
    [
      "4802670340679719",
      "327997117576655359374515"
    ],
    [
      "338780664106744",
      "4457435031894743807915"
    ],
    [
      "570931081927609",
      "1392606885066309435755"
    ],
    [
      "2583357643089094",
      "-124999491201269771521735"
    ],
    [
      "2253007628936104",
      "-100277589907893174528805"
    ],
    [
      "402265615162594",
      "957805848076257379640"
    ],
    [
      "1308742885990219",
      "39148345488185010200765"
    ],
    [
      "-950875158055406",
      "-6219604232915722584235"
    ],
    [
      "2335621805997169",
      "-106308883634360696501785"
    ],
    [
      "2826159087719839",
      "144168392305153246605275"
    ],
    [
      "-133095542249981",
      "17728927118916351270815"
    ],
    [
      "2435592855251131/4",
      "-30548405722480172927525/8"
    ],
    [
      "-29280710321774159/64",
      "10881571160052062865446605/512"
    ],
    [
      "10406853173250769",
      "1058256993787289135772815"
    ],
    [
      "1463307848164579",
      "-48107685339438911893825"
    ],
    [
      "1576440824146969",
      "-54938581478418935573485"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -25/31 of the rank-17 fibration of X1008 given in curve#3594. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-28 14:32:25",
  "updated_at": "2026-10-28 14:32:25"
}