{
  "id": 2840,
  "curve_key": "3935927231476504671580914402561:-7810268449519782435769838822064650529585645441",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-81998483989093847324602383387",
    "9039662557314583503984236650851472967245899"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    7
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  "naive_height": 211.34353704106135,
  "faltings_height": 15.332839294115056,
  "conductor": "3370525273093188329210",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "17",
    "53",
    "71",
    "139",
    "223",
    "617",
    "3027389"
  ],
  "discriminant": "-15500778873511975969237368396719961290510947157765742994373613651486760999485440000000",
  "regulator": "92395.8646525381893448549006239639721791967997984",
  "points": [
    [
      "120758100624827",
      "947965475556972223546"
    ],
    [
      "-117778126528243",
      "-4130799992267648976004"
    ],
    [
      "166003611484257",
      "47038619859647754246"
    ],
    [
      "292645587321907",
      "3178955262932679668346"
    ],
    [
      "-95474599855473557/289",
      "-1331648350736416603324902/4913"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Eroshkin (2009). Source: https://dujella.github.io/tors/z7old5.html (curve entry 11). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:24:49",
  "updated_at": "2026-09-26 20:24:49"
}