{
  "id": 2692,
  "curve_key": "6111138430132230232726561:-15107173980630815473141239414687269809",
  "ainvs": [
    "1",
    "0",
    "0",
    "-127315383961088129848470",
    "17485155070163945330435232719141412"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    9
  ],
  "naive_height": 171.2164661536764,
  "faltings_height": 11.786389074929016,
  "conductor": "1023209767452210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "107",
    "12619",
    "114299"
  ],
  "discriminant": "-29491232845915097376621080763420054932484854807738357463000000000",
  "regulator": "10845.191610897595571433216485265002878937767",
  "points": [
    [
      "10291765410186/49",
      "1090296499085007474/343"
    ],
    [
      "-55979284852881/196",
      "-479609533124397157833/2744"
    ],
    [
      "7648653205054401024924/24891688441",
      "337302481673686984286164322772798/3927186577025011"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "van Beek (2015). Source: https://dujella.github.io/tors/z9old3.html (curve entry 12). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:17:59",
  "updated_at": "2026-09-26 20:17:59"
}