{
  "id": 2874,
  "curve_key": "67815635404124359826113:-13205510475262743037713412474527265",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1412825737585924163044",
    "15284155642547476371073178165264"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "naive_height": 157.71323919574516,
  "faltings_height": 11.16283187882969,
  "conductor": "3909968370958694691318",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "29",
    "43",
    "47",
    "71",
    "431",
    "11351",
    "268993"
  ],
  "discriminant": "79569395352540341075395882036325863181216044329352639168799879424",
  "regulator": "225868.91960327324621549521101455562582648897806950",
  "points": [
    [
      "-4710088480",
      "-4672705304733532"
    ],
    [
      "10971680384",
      "1050627482515964"
    ],
    [
      "5142674960",
      "2855599110883388"
    ],
    [
      "190936944656",
      "81893102282965052"
    ],
    [
      "188694106912",
      "80419019486556004"
    ],
    [
      "47485021091/4",
      "3441975241405087/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella (2005). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 73). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:26:22",
  "updated_at": "2026-09-26 20:26:22"
}