{
  "id": 2709,
  "curve_key": "1544369062203823217041:-359564651557085889205745153564089",
  "ainvs": [
    "1",
    "0",
    "0",
    "-32174355462579650355",
    "416162791151353397699582660577"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    9
  ],
  "naive_height": 149.92489357649288,
  "faltings_height": 10.551065927245485,
  "conductor": "184371560352210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "47",
    "4519",
    "375787"
  ],
  "discriminant": "-72687095701612332271410771374105466234756967352238981000000000",
  "regulator": "3023.0688774409439905047301690238696815912196",
  "points": [
    [
      "166911654",
      "640934520337713"
    ],
    [
      "27386058757386/169",
      "143234884774188178041/2197"
    ],
    [
      "67307010402",
      "17411660303958525"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "van Beek (2015). Source: https://dujella.github.io/tors/z9old3.html (curve entry 11). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:18:43",
  "updated_at": "2026-09-26 20:18:43"
}