{
  "id": 5337,
  "curve_key": "509040:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-10605",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 39.42084563372002,
  "faltings_height": 1.353310881118159,
  "conductor": "3598912800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "101"
  ],
  "discriminant": "76332940488000",
  "regulator": "71.29286774053252313852017820637084825742284939",
  "points": [
    [
      "-101",
      "202"
    ],
    [
      "-84",
      "546"
    ],
    [
      "169",
      "1742"
    ],
    [
      "505",
      "11110"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny endpoint from the Aguirre–Castañeda–Peral parametrization at tuple (4,7,16,27), 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 13:54:45",
  "updated_at": "2026-10-21 13:54:45"
}