{
  "id": 5269,
  "curve_key": "-31824144:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "663003",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 51.82720741485759,
  "faltings_height": 2.387174362879623,
  "conductor": "1562926144032",
  "bad_primes": [
    "2",
    "3",
    "11",
    "37",
    "181"
  ],
  "discriminant": "-18652045000889665728",
  "regulator": "555.758710685708808310169048176270878878501880590",
  "points": [
    [
      "37",
      "4958"
    ],
    [
      "111",
      "8658"
    ],
    [
      "181",
      "11222"
    ],
    [
      "192",
      "11592"
    ],
    [
      "543",
      "22806"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (3,4,9,16), 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 11:38:44",
  "updated_at": "2026-10-21 11:38:44"
}