{
  "id": 2841,
  "curve_key": "1736666875676959967261591004961:-2292715294494700546961676881289159668710997041",
  "ainvs": [
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    "0",
    "0",
    "-36180559909936665984616479270",
    "2653605664924418914307133525288436083708900"
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  "rank_lower_bound": 5,
  "torsion": [
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  "naive_height": 208.89213203601923,
  "faltings_height": 15.202660714967498,
  "conductor": "887644055522613612630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "29",
    "31",
    "59",
    "151",
    "337609",
    "994769"
  ],
  "discriminant": "-10842342311707233347442439474925484506204284929600955722084264520855441137500160000000",
  "regulator": "61550.5955432289476463936806509220441089963984636",
  "points": [
    [
      "47596634272620",
      "1019490087452772331530"
    ],
    [
      "65357521331220",
      "753734338701716054250"
    ],
    [
      "37071254323980",
      "1167601425603747441930"
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    [
      "110821323250140",
      "71171122159540704330"
    ],
    [
      "20835879745863744/169",
      "568498652465192600946354/2197"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z7old5.html (curve entry 9). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:24:52",
  "updated_at": "2026-09-26 20:24:52"
}