{
  "id": 5229,
  "curve_key": "611691696:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-12743577",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 60.69521684651594,
  "faltings_height": 3.126175148851152,
  "conductor": "11784036626208",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "37",
    "71"
  ],
  "discriminant": "132450626299107445826112",
  "regulator": "289.471490977468886254403248187119667462581338913",
  "points": [
    [
      "-3108",
      "97902"
    ],
    [
      "-2331",
      "130536"
    ],
    [
      "-1221",
      "117216"
    ],
    [
      "8547",
      "717948"
    ],
    [
      "25641/4",
      "3410253/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (4,5,14,20), 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 following the parametrization search 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 10:38:53",
  "updated_at": "2026-10-21 10:38:53"
}