{
  "id": 5312,
  "curve_key": "-1212203664:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "25254243",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 62.74711725024127,
  "faltings_height": 3.297166849161596,
  "conductor": "2267650807121952",
  "bad_primes": [
    "2",
    "3",
    "7",
    "31",
    "67",
    "193"
  ],
  "discriminant": "-1030820481399670315962048",
  "regulator": "9996.9880233676226972689261903952373018456480965614",
  "points": [
    [
      "193",
      "69866"
    ],
    [
      "1953",
      "238266"
    ],
    [
      "2412",
      "273762"
    ],
    [
      "5425",
      "544670"
    ],
    [
      "51724",
      "11818934"
    ],
    [
      "523404",
      "378682794"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (6,11,18,22), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3.",
  "created_at": "2026-10-21 13:02:50",
  "updated_at": "2026-10-21 13:02:50"
}