{
  "id": 3041,
  "curve_key": "3555849734018545788360833600200321:-211820483225080625229117632697010215254835333432769",
  "ainvs": [
    "1",
    "0",
    "0",
    "-74080202792053037257517366670840",
    "245162596325324791545535916283786496196278857792"
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  "rank_lower_bound": 8,
  "torsion": [
    4,
    2
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  "naive_height": 231.76170638561146,
  "faltings_height": 17.087950826703775,
  "conductor": "812040122999528003685943162590",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "23",
    "37",
    "67",
    "97",
    "107",
    "113",
    "181",
    "353",
    "757",
    "797",
    "1500073"
  ],
  "discriminant": "53522188574629790367338571328926126150913249648354604215545060828773434442761454048709417369600",
  "regulator": "27241955.4676389454962231578788778750436717627103715468",
  "points": [
    [
      "4788825441078024",
      "15061463188506846389448"
    ],
    [
      "2502112947834762",
      "274718423698114510009170"
    ],
    [
      "3013816380468554",
      "221975741815687460563748"
    ],
    [
      "-2519466817783248",
      "-644835137924363889045240"
    ],
    [
      "5855963060746032",
      "110300164969468654954440"
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    [
      "9872268963343724",
      "689920984075167459213848"
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    [
      "5101321879516304",
      "3132086030194574751848"
    ],
    [
      "-3629653943551056",
      "-682810094828549484558072"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2012). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 6). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:33",
  "updated_at": "2026-09-26 20:34:33"
}