{
  "id": 4569,
  "curve_key": "168140092272217:-2180253147468950278621",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3502918589005",
    "2523440850993995220"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 98.26745589125285,
  "faltings_height": 5.434200370246598,
  "conductor": "2217675371622802",
  "bad_primes": [
    "2",
    "7",
    "13",
    "163",
    "223",
    "3529",
    "7307"
  ],
  "discriminant": "40021456367284036320053924",
  "regulator": "65064.107567394842396886361117038934690559107979676",
  "points": [
    [
      "4329707/4",
      "22370067/8"
    ],
    [
      "1080577",
      "-534206"
    ],
    [
      "136737033/121",
      "118736079652/1331"
    ],
    [
      "4020817609/3721",
      "-122288618388/226981"
    ],
    [
      "55799130/49",
      "36058160510/343"
    ],
    [
      "963895819/900",
      "450480508193/27000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z3.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Six supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C3. Source-attributed existing curve.",
  "created_at": "2026-10-18 02:05:27",
  "updated_at": "2026-10-18 02:05:27"
}