{
  "id": 3206,
  "curve_key": "17638060551971673221835110328184062481:-18994747761520743166661145882355695051860527528290054265",
  "ainvs": [
    "1",
    "0",
    "0",
    "-367459594832743192121564798503834635",
    "21984661761019378634495434090738640299893358837979121"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
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  "naive_height": 257.2893673388593,
  "faltings_height": 19.50490031256304,
  "conductor": "7210387210131632436261753944550733665686372892278111682534",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "19",
    "23",
    "29",
    "103",
    "107",
    "113",
    "241",
    "311",
    "367",
    "569",
    "743",
    "2731",
    "4027",
    "18539",
    "30931",
    "83891"
  ],
  "discriminant": "2966678824492889969226683679546865785807244790410849948256562594250559795589427442837666952195201464713347072",
  "regulator": "8526995337068307.9000731223937026900529113241711794800465552992841143",
  "points": [
    [
      "-500948227073954754",
      "-283461415913825633855972799"
    ],
    [
      "618831961967068686",
      "-177686449752803041027303839"
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    [
      "354928123930978469646/121",
      "-6545314995386561940741799315149/1331"
    ],
    [
      "-2206972301687051310354/3721",
      "-40146036579517558974806417628507/226981"
    ],
    [
      "96978527597450937582/169",
      "-19794967659002871547033313259/2197"
    ],
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      "24133730276980682677278/22801",
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    ],
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      "26884132496771856140286",
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      "-874693212297438935973657704142944295625697876370825/59212212373798163147287"
    ],
    [
      "-62297171251806603124327393276525746/265374217511812201",
      "-42204302612827000938418408024464108397522795494479445/136706161739364087024127051"
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      "4002066240510226668213767537520/3513379108801",
      "-6848347445308257354081202217984738422231299849/6585481314915703201"
    ],
    [
      "2350416733051927950115826110434201/2659406316802624",
      "-85381085358082707435273755345112637793036795986215/137144073214723375789568"
    ],
    [
      "699961735935344351725016081120/12034509108241",
      "-1187390285943810459533203811514224168328759761/41748662822707580039"
    ],
    [
      "927626820258076427035790768764821679587536769093296430/901877235416925889645906354909317481",
      "-732863137447335689322724697343858529212680408266021158446740446589129931914847541/856487713579780479973721374503834453454776890490994379"
    ],
    [
      "270863294703076866521299118006000296/68870806034085441",
      "-139310777790545108701048182959835028974454064842628783/18073936358253200779438239"
    ],
    [
      "-867150520287461633971046341666445590678146/3207346736264459038483249",
      "-1830632199455553382055683577064412216922741341445055656264538729/5744058694869399174638953537009774807"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-046, rational kernel x=5073086876276604943/4. 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 20:42:37",
  "updated_at": "2026-09-26 20:42:37"
}