{
  "id": 4992,
  "curve_key": "-4331980224:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "90249588",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 66.56787180293335,
  "faltings_height": 3.615563061885936,
  "conductor": "1809997363148832",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "47",
    "373"
  ],
  "discriminant": "-47045236695917319556190208",
  "regulator": "2215.82471135124844134945262101169169650195449153",
  "points": [
    [
      "286",
      "160732"
    ],
    [
      "1222",
      "334828"
    ],
    [
      "2574",
      "499356"
    ],
    [
      "3364",
      "584524"
    ],
    [
      "8272",
      "1145672"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #4991: https://elliptic-rank.icarm.cloud/curve/4991. 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:32:22",
  "updated_at": "2026-10-21 01:32:22"
}