{
  "id": 3223,
  "curve_key": "703401089752319796935813242538898793825:-16423671178893990534345656361494066780703772072656121140625",
  "ainvs": [
    "1",
    "0",
    "0",
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    "19008878679275452006123327230168503570949134500981218692"
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  "rank_lower_bound": 16,
  "torsion": [
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  "naive_height": 268.3469718512651,
  "faltings_height": 20.345086029232167,
  "conductor": "1518905128450311243438362902929463593569897853087633327924112350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "53",
    "127",
    "137",
    "139",
    "193",
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    "503",
    "1901",
    "3853",
    "4703",
    "13633",
    "34693",
    "259717",
    "491423"
  ],
  "discriminant": "45304952459165919255314382335478619447459560354533223479690941713480522086892861457677617226875150545453056000000",
  "regulator": "6974572572755664.499920951057816769606883148859314691362567056748818924",
  "points": [
    [
      "7015812266231410952",
      "16171811732325153037621844474"
    ],
    [
      "14202884310794403716",
      "51729201166903825510053456830"
    ],
    [
      "221106882359692226276/25",
      "3013545121128313237963976102086/125"
    ],
    [
      "-434063802263819801692/4489",
      "1359267799692517323052016067033482/300763"
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      "14968584146028372685508/5329",
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    ],
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      "2437398173762165019908/529",
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      "-4258433397283870514845653854648072333207090/938687580627497"
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      "885540984542806805856343100936509402177988/270794398061696264662729",
      "-346843113118600010903691434706419241447686012503767332519866262/140915742636227615860196473287763067"
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      "833000864701173232149412/292681",
      "94456467390189919734712764944416054/158340421"
    ],
    [
      "2433688872161372860420327268/1628687449",
      "43998230115629446979209903415390780368262/65728939379293"
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    [
      "-14413561802736011430288081628/27175852201",
      "23119399194928291062145500522223526505419114/4479966411187051"
    ],
    [
      "-2653276064290069948",
      "6261929395060343278047486974"
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    [
      "-544142855172799897337508832586547187/194753234537868304",
      "530793161032312869765101345570159634542925926814300113/85946267152210112253462592"
    ],
    [
      "64302877790389736062226468/46199209",
      "359229975375128000428252646351787742102/314016023573"
    ],
    [
      "196316187418090315535341310482/13530575041",
      "-84180982943941897394578146396621435502671886/1573890019344161"
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    [
      "-6258434090598455032879975294449052/2141316115763449",
      "601688847960410735735577433060955309110099243478182/99088026390691166577293"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-027, rational kernel x=-12420185912395920417/4. 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 20:43:25",
  "updated_at": "2026-09-26 20:43:25"
}