{
  "id": 2857,
  "curve_key": "78920330158760496442339164481:-25180481508909249002023322233889210031921121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1644173544974177009215399260",
    "29144075820496678960101949181880262179600"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    7
  ],
  "naive_height": 199.8692861137128,
  "faltings_height": 14.637035294826328,
  "conductor": "298298673786012728010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "31",
    "61",
    "83",
    "34483",
    "46199"
  ],
  "discriminant": "-82469793783287598516267317999532844672521668550211278574722191517557792440320000000",
  "regulator": "18019.9202265926705618855016333184143408715134324",
  "points": [
    [
      "18840522713400",
      "69675800769119471460"
    ],
    [
      "-5279882261448",
      "-194108035447655037084"
    ],
    [
      "28556991474360",
      "74025000283910777700"
    ],
    [
      "14185096013112",
      "93142882933735615332"
    ],
    [
      "-16480379716140",
      "-227518256916697261800"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Elkies (2006). Source: https://dujella.github.io/tors/z7old5.html (curve entry 4). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:25:33",
  "updated_at": "2026-09-26 20:25:33"
}