{
  "id": 742,
  "curve_key": "123578131007788916715489349075910080081:-1373883364962299798974608593719782985811955201937520450521",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2574544395995602431572694772414793335",
    "1590142783521180322672733098620485660577223586022749225"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 263.12998320727905,
  "faltings_height": 19.618504665492452,
  "conductor": "578428639984362476094839549654682846384775913940539978193809925490248572670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "31",
    "73",
    "83",
    "89",
    "109",
    "211",
    "229",
    "8237",
    "157159319",
    "4481778631002221601761",
    "10046866790448265616569"
  ],
  "discriminant": "-188276824185236699074697649198046544797560571814523252727185629091630037535751953678619982561738733568000000",
  "regulator": "89612332731499927945.930879657378311461979382236353148117973442872315021250559823",
  "points": [
    [
      "-1116194618116980740",
      "-1753048542612704384302902875"
    ],
    [
      "3901133798208439836605/21904",
      "-3457127812655114447796930752324245/3241792"
    ],
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      "-80764463198966039221039435"
    ],
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      "925370031426195742",
      "-11827270663881164879007899"
    ],
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      "927582477435021170",
      "-11876885897491734411403135"
    ],
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      "934756649775495830",
      "-18237373299467504763464395"
    ],
    [
      "942529381285708070",
      "-29427686006039397366296635"
    ],
    [
      "980558949703449620",
      "-91943457070211226178812235"
    ],
    [
      "4084690114456231775/4",
      "-1288985403905662391374835195/8"
    ],
    [
      "1035165746259221270",
      "-185238299681285550869858635"
    ],
    [
      "1104753899596237670",
      "-306979094114644274237750635"
    ],
    [
      "1658474571182554070",
      "-1371868631570175632106986635"
    ],
    [
      "763461662713934141350/441",
      "-14110878077486290471360203848815/9261"
    ],
    [
      "7557393901746312062",
      "-20341283714330006674225398619"
    ],
    [
      "32956323755350021270",
      "-188974181066107220389210962635"
    ],
    [
      "295520153816963777270",
      "-5080123473497357112408566966635"
    ],
    [
      "6610176389941686085510/9",
      "-537425831956531757999216713628585/27"
    ],
    [
      "849654256744809110",
      "-126673141070283577607190475"
    ],
    [
      "926088525148392070",
      "-11716793797166084288585435"
    ],
    [
      "50151813630880722550",
      "-354985260154762044042190975115"
    ],
    [
      "924844521998451350",
      "-11983394182984115458099915"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=17/106 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 21 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 18:15:11",
  "updated_at": "2026-09-16 18:15:11"
}