{
  "id": 4353,
  "curve_key": "3257327817:-186337664237061",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-67860996",
    "215685558116"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 65.71716308584071,
  "faltings_height": 3.2815069135428474,
  "conductor": "1403913962178",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "29",
    "67",
    "2131"
  ],
  "discriminant": "-93099521910157553736036",
  "regulator": "160.077531395498631802883765364251818494147396280",
  "points": [
    [
      "4894",
      "25360"
    ],
    [
      "2866",
      "210064"
    ],
    [
      "1904",
      "304626"
    ],
    [
      "-2006",
      "587296"
    ],
    [
      "32011",
      "5537770"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "BASE torsion/torsion_Z3.tsv.gz:154 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 10:05:57",
  "updated_at": "2026-10-17 10:05:57"
}