{
  "id": 5063,
  "curve_key": "-4706556624:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "98053263",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 66.81666719970032,
  "faltings_height": 3.636296011616517,
  "conductor": "697646612966688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "29",
    "41"
  ],
  "discriminant": "-60334556657252608195996608",
  "regulator": "2969.15696632031502278792735332622344100940848442",
  "points": [
    [
      "697",
      "262072"
    ],
    [
      "6273",
      "928404"
    ],
    [
      "34153/4",
      "9665299/8"
    ],
    [
      "222343/9",
      "112950244/27"
    ],
    [
      "853825/16",
      "802424735/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,12,27,36), 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 01:55:42",
  "updated_at": "2026-10-21 01:55:42"
}