{
  "id": 5076,
  "curve_key": "1560111963696:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-32502332577",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 84.2273361186436,
  "faltings_height": 5.087185088195124,
  "conductor": "33804851934269294749728",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "19",
    "37",
    "47",
    "2293"
  ],
  "discriminant": "2197473080567724722869798872578112",
  "regulator": "743056.46334424658521923848644224393220714350957064",
  "points": [
    [
      "-13959",
      "21236292"
    ],
    [
      "323313",
      "152603736"
    ],
    [
      "-182236175/1024",
      "398439029065/32768"
    ],
    [
      "-19943/36",
      "916543243/216"
    ],
    [
      "2909817/16",
      "652768947/64"
    ],
    [
      "107861098423/582169",
      "8166438077819944/444194947"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,4,31,60), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 02:13:25",
  "updated_at": "2026-10-21 02:13:25"
}