{
  "id": 5001,
  "curve_key": "332225568:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-6921366",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 58.86397415359526,
  "faltings_height": 2.973571591107762,
  "conductor": "3065939667581184",
  "bad_primes": [
    "2",
    "3",
    "43",
    "139",
    "193"
  ],
  "discriminant": "21220490573247709177344",
  "regulator": "3643.79758852206693412479718826405390829083250162",
  "points": [
    [
      "-2322",
      "59598"
    ],
    [
      "-1112",
      "79508"
    ],
    [
      "-258",
      "42054"
    ],
    [
      "-386/9",
      "465130/27"
    ],
    [
      "15609/4",
      "1440285/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,8,9,28), 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. Selected in a bounded tuple search using a small-prime sieve and height screening, following the search approach described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:46:12",
  "updated_at": "2026-10-21 01:46:12"
}