{
  "id": 2173,
  "curve_key": "11757206041:-275517010545661",
  "ainvs": [
    "1",
    "0",
    "1",
    "-244941793",
    "318865017056"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 69.56319650892692,
  "faltings_height": 3.8622731792275067,
  "conductor": "6507930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "37",
    "41"
  ],
  "discriminant": "896592149773469856698062500",
  "regulator": "6.72047630415166334083307881045590206836068",
  "points": [
    [
      "-1685/4",
      "5198431/8"
    ],
    [
      "-20",
      "569012"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Height-ordered search of the universal family for torsion Z/2Z x Z/6Z (Tate/Kubert normal form, parameter t=35/13), smallest curves first; rank lower bound from PARI ellrank: 2 independent points.",
  "created_at": "2026-09-26 14:55:46",
  "updated_at": "2026-09-26 14:55:46"
}