{
  "id": 3074,
  "curve_key": "8477791390754804550876678081:-780550278995895323259069698168977888653729",
  "ainvs": [
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    "-1",
    "1",
    "-176620653974058428143264127",
    "903414674763811890417046406006315779751"
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  "rank_lower_bound": 9,
  "torsion": [
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  "naive_height": 192.92174243255045,
  "faltings_height": 13.753208388144909,
  "conductor": "110072036541366600851273211270",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "37",
    "41",
    "59",
    "67",
    "257",
    "3203",
    "48539",
    "173659"
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  "discriminant": "37680625595733672595162394125080255054776863668468923554151621660697600000000",
  "regulator": "41591232.551277112363905114446882573145299362399599645153",
  "points": [
    [
      "7768993064691",
      "406346675232305014"
    ],
    [
      "4347401613651",
      "14755987046504074774"
    ],
    [
      "8207792508501",
      "2586575356972455874"
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    [
      "7770133855251",
      "412584154102196374"
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    [
      "15728276331",
      "30010610452491148414"
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    [
      "249263407251",
      "29315611689872948374"
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    [
      "4777788280851",
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    [
      "7865802003931",
      "902972932760584854"
    ],
    [
      "7764585247251",
      "382035197041964374"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 42). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:36:02",
  "updated_at": "2026-09-26 20:36:02"
}