{
  "id": 5271,
  "curve_key": "1056386016:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-22008042",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 62.33435850266869,
  "faltings_height": 3.2627702868638813,
  "conductor": "3444294490124544",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "29",
    "317"
  ],
  "discriminant": "682219600191265946245632",
  "regulator": "6963.5217077078636442703882662254855369380350009688",
  "points": [
    [
      "-4598",
      "63118"
    ],
    [
      "-4256",
      "128744"
    ],
    [
      "-3857",
      "165851"
    ],
    [
      "-342",
      "86526"
    ],
    [
      "4698",
      "17226"
    ],
    [
      "14616",
      "1673532"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (3,8,10,12), 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 11:41:48",
  "updated_at": "2026-10-21 11:41:48"
}