{
  "id": 748,
  "curve_key": "23713159824685004017515006488805961123072576:-112262529386539042193520788567144096642471233800005685251527394176",
  "ainvs": [
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  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 299.62381219995524,
  "faltings_height": 22.88005899144392,
  "conductor": "13713792420445736434908008709350792188822397906478024811690216268911099779951692892301792169222456244028191480",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "67",
    "103",
    "823",
    "3121",
    "4483",
    "252702087248153",
    "614730522279708207905232553732673",
    "4979995603879699209645396858755060879856491"
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  "discriminant": "423243655651351406628133403780642405167779882423177982068223504595709799732797179183781464989125500213729402499610463124000000",
  "regulator": "34924277214770449210447732858.87680756907389055736378006454677912804015163376072044821873",
  "points": [
    [
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      "-13701598765641475899165122947650"
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      "-1673889334475252691417304959/7134241",
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    ],
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      "-100921979472888703622431753304469793/3375"
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      "-298113010440527248555029843028770"
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      "6745673506463149626931",
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      "649209924463259499161041/16",
      "-523013596859165620595108356483921215/64"
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      "-14521107134264297384940766273574010"
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    [
      "225183098030987346277486",
      "-106856654135044580121036378188671335"
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    [
      "16481463156809408638646546572561/60466176",
      "-66910180804393672796126121188467286965199919865/470184984576"
    ],
    [
      "309629198586173493764286",
      "-172290664100435436137639096244448815"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-16 19:31:42"
    }
  ],
  "commentary": "Specialization T=-265/221 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 25 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 19:04:16",
  "updated_at": "2026-09-16 19:31:42"
}