{
  "id": 3208,
  "curve_key": "54368249023419599483629274477765281:-47919663892131552494092430343443010897706114804990321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1132671854654574989242276551620110",
    "55462573949226333810810250935548161657710883204100"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
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  "naive_height": 242.60273136508354,
  "faltings_height": 18.272565263325987,
  "conductor": "20373912393913499123029748197579404326128537369302233310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "41",
    "103",
    "179",
    "191",
    "197",
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    "227",
    "311",
    "479",
    "1069",
    "1193",
    "1303",
    "2879",
    "7019",
    "27539"
  ],
  "discriminant": "-1235871948351333157788553973646409235009709305211957790300819362578280483547373501185848013209600000000",
  "regulator": "25967003120194962.348422958752708158897845160095334827961321517828940",
  "points": [
    [
      "-44399520153394180",
      "4269322522045548266957090"
    ],
    [
      "-16104057183193780",
      "-8338270165304701692657310"
    ],
    [
      "-336200071819985120/9",
      "-182418505127661725175658570/27"
    ],
    [
      "492042086877295196/25",
      "798374836975700144709964954/125"
    ],
    [
      "-47593132835631680",
      "1251587532590658638294590"
    ],
    [
      "-1278875587644430514420/27889",
      "15431653625213912567737466704670/4657463"
    ],
    [
      "9076943795353383980/169",
      "26868635567219558879763609530/2197"
    ],
    [
      "28243904918565163749020/866761",
      "5883235846913944976698254990991190/806954491"
    ],
    [
      "-1866826522319934986019880/200817241",
      "-22976700017256170295285750341515594010/2845781122211"
    ],
    [
      "1910991823544030487326396/9247681",
      "-2614858509844886006007285613664770718/28122197921"
    ],
    [
      "-80599034327317826711084455780/1734649677721",
      "-6372022438776303296786920362366166992692710/2284639439188897981"
    ],
    [
      "119038406297655119374675319810770/320948980672401",
      "-1294115917096991153869721932685104979544474106840/5749816715246116862649"
    ],
    [
      "906306091152487017282620/19088161",
      "869562334446665031457171563863303810/83396175409"
    ],
    [
      "-3547140396541630684528708020108728391280779620/75462925786059118895218342009",
      "-45640361295304700342344614634657594360285469182638415991101730728570/20730055219623497863241384173728710603039027"
    ],
    [
      "173878499096521132422620/4932841",
      "-84391290818273251369307699620123510/10955839861"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-044, rational kernel x=382942867905233439/4. 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 20:42:44",
  "updated_at": "2026-09-26 20:42:44"
}