{
  "id": 5309,
  "curve_key": "21216:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-442",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 29.887532678956767,
  "faltings_height": 0.5588681348878877,
  "conductor": "12503296",
  "bad_primes": [
    "2",
    "13",
    "17"
  ],
  "discriminant": "5526456832",
  "regulator": "17.184543068123298738064705283662758366085413",
  "points": [
    [
      "-17",
      "51"
    ],
    [
      "-9",
      "57"
    ],
    [
      "-1",
      "21"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (1,2,19,22), 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 12:57:46",
  "updated_at": "2026-10-21 12:57:46"
}