{
  "id": 4130,
  "curve_key": "66716727314794618779268416391457058674521:-27016207526017239000855293957778206669472241878811640371711069",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1389931819058221224568092008155355389053",
    "31268758710668100695318540355099554098730716729426452295948"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 282.90308508858647,
  "faltings_height": 21.608201676242754,
  "conductor": "4314840781331577048533982362444226180847473271945109203486392757751509762883515395627329659613705975331330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "31",
    "3001",
    "119831216174217960033270873519462043",
    "63555015044788012585684111936661836657486223912739261314772689"
  ],
  "discriminant": "-250527312583916610737967422281900878165744280161937646698986212727951060566825820758302156847006805311918556974189062500",
  "regulator": "359087157220808323009832048060.936418382730185794264020863223919616906103422424287793253574",
  "points": [
    [
      "30966147068942497649",
      "-133870960745661716903409393450"
    ],
    [
      "-41348946710236762213",
      "-134332489462530028097645996268"
    ],
    [
      "23024657545057022149",
      "107108487310893596450609696300"
    ],
    [
      "43582499655292433714",
      "-231244782392282148391901539710"
    ],
    [
      "-3211592811572101",
      "-176842366546235379325976035200"
    ],
    [
      "5199844624287472649",
      "155505384500673488017679620800"
    ],
    [
      "95534421153001386224",
      "877729132422659177061536575500"
    ],
    [
      "13911711296587462049",
      "-120933210754781603840569063800"
    ],
    [
      "229621741478943008231/4",
      "-3000288746944628783022968829915/8"
    ],
    [
      "75535333247636317049",
      "-597706598977862313203628415050"
    ],
    [
      "-179064811783544602034/9",
      "-6100268205829536404294529509150/27"
    ],
    [
      "61309848820464442274",
      "420130563360165985774328596050"
    ],
    [
      "3345308520098747529074",
      "-193476167049459361882313230943925"
    ],
    [
      "84126703729163063324",
      "713952721434954935490212753475"
    ],
    [
      "-6553559837062003351",
      "-200240580935041957016117335200"
    ],
    [
      "97715416008455349676904/3721",
      "-25758169893539018446794928224087900/226981"
    ],
    [
      "-7037505299474175226",
      "-201747040574085290463013208325"
    ],
    [
      "10989650803467243587909/16",
      "1150419265443654982618203778739175/64"
    ],
    [
      "2330949596334615543524",
      "112523777496483744506745500916675"
    ],
    [
      "3657891257351755603637/361",
      "-925974589141668274962371233989492/6859"
    ],
    [
      "469603404264671418524",
      "-10145883390306512692677679163325"
    ],
    [
      "131084426706615303254",
      "-1449658816835554064980303353285"
    ],
    [
      "93428523905217832274",
      "846721147982899874419662441675"
    ],
    [
      "8148228613865743681421/529",
      "1414409663312248258706608108317900/12167"
    ],
    [
      "20318276365653757154",
      "-106844661797514388339560371445"
    ],
    [
      "51149183195095111239146/4489",
      "39111615761962504587078529659947145/300763"
    ]
  ],
  "submitter": "apkorte",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-10 11:29:53"
    }
  ],
  "commentary": "Specialization at T = 799/404 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": "2026-10-10 11:14:43",
  "updated_at": "2026-10-10 11:29:53"
}