{
  "id": 3201,
  "curve_key": "61269735183859028632784836109191080241:-479556992536016917495896844310857252422326870437462298665",
  "ainvs": [
    "1",
    "0",
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    "555042815435204765513879909184107302630960204020457961"
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  "rank_lower_bound": 15,
  "torsion": [
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  "naive_height": 261.025048057189,
  "faltings_height": 19.435007293379964,
  "conductor": "6354102106121224871907639158710170892231970450727352086832662",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "19",
    "43",
    "73",
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    "103",
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    "569",
    "773",
    "1013",
    "1543",
    "1823",
    "17093",
    "59341",
    "2236139"
  ],
  "discriminant": "17638273190245233438550034825367779352190209051980746192715738540577179286729536390940540532029522582700032",
  "regulator": "327020041757641968.78496504085444527963887101009502143024346334682319",
  "points": [
    [
      "238649557677636890906/361",
      "73558233921924458656981323017/6859"
    ],
    [
      "112191852604278305342/169",
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      "6285687175612217254442/5329",
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    ],
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      "89705408122534677738314/134689",
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      "10947248534856026953146218/361201",
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      "7254414405909497565297908035082/11022818323969",
      "-200634069531027008966802719464432933038913019/36596451273131490047"
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      "32578991253238388305070477377639276344618712298/53353189428410587401463604401",
      "706613194800970595262843641524630960627157673096895933771907218336243/12323684735980821904664850986898183358666601"
    ],
    [
      "61679230743735683700930730973927930/762462913278361",
      "-15316738231126276138189862585017682985213450292498511/21053683321831710413891"
    ],
    [
      "413096357667474290096855337332846589482/660647722244928765649",
      "628576098602956338137689699168873473858827685428550674941/16980673555508685448642877749607"
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      "42301857508751868564118860609657194812473725001242/62531020076992654518284376576169",
      "-16575198593867131635669915679234811213396334620697560163741495984385602793/494473782902670389662206850949553938158066172053"
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  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-041, rational kernel x=-5183611506357375057/4. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:42:26",
  "updated_at": "2026-09-26 20:42:26"
}