{
  "id": 6196,
  "curve_key": "10045033705:-1007243843821813",
  "ainvs": [
    "1",
    "0",
    "1",
    "-209271536",
    "1165774046610"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 69.09198825622835,
  "faltings_height": 3.504798045403377,
  "conductor": "35858678834",
  "bad_primes": [
    "2",
    "11",
    "19",
    "37",
    "61",
    "191",
    "199"
  ],
  "discriminant": "-560831625838385811301348",
  "regulator": "633.628809154283738282911378738377566118736639233",
  "points": [
    [
      "2226",
      "842075"
    ],
    [
      "8881",
      "83405"
    ],
    [
      "247064",
      "122475070"
    ],
    [
      "865771/81",
      "278543197/729"
    ],
    [
      "2979771/361",
      "165150927/6859"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 81/191 of the elliptic fibration of X648 given by:\ny^2 + (Lx+B)y = x^3,\nwhere\nL = -91T^2 + 72T - 81,\nB = -81000T^5 + 243000T^4 - 243000T^3 + 81000T^2.",
  "created_at": "2026-10-30 15:41:06",
  "updated_at": "2026-10-30 15:41:06"
}