{
  "id": 4991,
  "curve_key": "1082995056:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-22562397",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 62.40898871957368,
  "faltings_height": 3.2689894716059635,
  "conductor": "1809997363148832",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "47",
    "373"
  ],
  "discriminant": "735081823373708118065472",
  "regulator": "1107.91235567562422067472631050584584825097724576",
  "points": [
    [
      "-4653",
      "65142"
    ],
    [
      "-3357",
      "194706"
    ],
    [
      "-1551",
      "176814"
    ],
    [
      "20163",
      "2782494"
    ],
    [
      "80652",
      "22864842"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (11,22,38,41), 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 01:30:55",
  "updated_at": "2026-10-21 01:30:55"
}