{
  "id": 750,
  "curve_key": "1567198017257634225181201328961484677696:-98970450281943209721015789361351374186161320959491602832256",
  "ainvs": [
    "0",
    "0",
    "0",
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    "114549132270767603843768274723786312715464491851263429204"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 271.68434324848,
  "faltings_height": 20.67454027362374,
  "conductor": "3167944256312105589192172798619147853260732573731118451476838945462641112466843594300635282197096040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "61",
    "27917",
    "25348867",
    "1794770750633232006834898747541241599",
    "2531748732023294652052588230419412211917443"
  ],
  "discriminant": "-3440937438703068968684090868085792603456772255093702604465517098908181497235811840986312588565292106033087468000000",
  "regulator": "236403719584611619017433856.76443039660508056189183059582760711018450513755793301356398",
  "points": [
    [
      "-5619538686295238007",
      "-10980264915434569640811260895"
    ],
    [
      "-4958460290803274922",
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    ],
    [
      "-4485259444357636422",
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    ],
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      "31554822478559844033/5476",
      "-4333453232129446781558573540523585/405224"
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    [
      "2610357230433880352938/441",
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    ],
    [
      "667851180087847327602/49",
      "-16093492120009975318996829778270/343"
    ],
    [
      "60670910042735168958",
      "-470596216016083454868892769910"
    ],
    [
      "110944670598686266578",
      "-1167081440524606432050260260050"
    ],
    [
      "4761307941001969949553/16",
      "-328481014931778031345356184727415/64"
    ],
    [
      "374537772689708720580",
      "-7247585737463636417340742252362"
    ],
    [
      "769239689243512935628",
      "-21334408102179131433721243371550"
    ],
    [
      "1247952848653737486553",
      "-44085190869867927325562933839975"
    ],
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      "1451370384383227100553",
      "-55292220054306585930389505306975"
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    [
      "2704275344818780993098",
      "-140629163923592540217476272002510"
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  ],
  "submitter": "Valery Asiryan",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-16 19:35:07"
    }
  ],
  "commentary": "Specialization T=-83/111 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 24 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 19:05:30",
  "updated_at": "2026-09-16 19:35:07"
}