{
  "id": 4349,
  "curve_key": "108419635648:-23000610359168000",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-2258742409",
    "26621829718729"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 76.22782515063652,
  "faltings_height": 4.388654183363842,
  "conductor": "656795382758592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "29",
    "43",
    "61",
    "67",
    "379"
  ],
  "discriminant": "431380174813005369419749822464",
  "regulator": "1771.6931811210896756374316286309963254912369867042",
  "points": [
    [
      "45199",
      "4106844"
    ],
    [
      "347641",
      "203113680"
    ],
    [
      "40705",
      "1456728"
    ],
    [
      "-1983",
      "5576120"
    ],
    [
      "-18179/4",
      "48526023/8"
    ],
    [
      "-7175",
      "6516048"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-17 10:08:34"
    }
  ],
  "commentary": "BASE torsion/torsion_Z2xZ2.tsv.gz:138 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 10:05:49",
  "updated_at": "2026-10-17 10:08:34"
}