{
  "id": 5266,
  "curve_key": "-31333584:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "652783",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 51.7806031546025,
  "faltings_height": 2.3832906745250324,
  "conductor": "13636020642848",
  "bad_primes": [
    "2",
    "17",
    "19",
    "43",
    "47"
  ],
  "discriminant": "-17802724926600491968",
  "regulator": "1534.17729313518990714817828409807858788810290411",
  "points": [
    [
      "17",
      "3332"
    ],
    [
      "188",
      "11374"
    ],
    [
      "752",
      "30268"
    ],
    [
      "1175",
      "48880"
    ],
    [
      "12032",
      "1322768"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (2,4,5,7), 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 11:34:15",
  "updated_at": "2026-10-21 11:34:15"
}