{
  "id": 5092,
  "curve_key": "-2614464:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "54468",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 44.32970898945707,
  "faltings_height": 1.7623828274295796,
  "conductor": "659280672",
  "bad_primes": [
    "2",
    "3",
    "17",
    "89"
  ],
  "discriminant": "-10341993497038848",
  "regulator": "38.742787245946291391085873824392325366818666",
  "points": [
    [
      "64",
      "1936"
    ],
    [
      "178",
      "3916"
    ],
    [
      "178/9",
      "28124/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,9,33,45), 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 by height screening in a bounded tuple search, following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.",
  "created_at": "2026-10-21 02:36:10",
  "updated_at": "2026-10-21 02:36:10"
}