{
  "id": 5196,
  "curve_key": "53856:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1122",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 32.6822072909716,
  "faltings_height": 0.7917576858891235,
  "conductor": "80568576",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17"
  ],
  "discriminant": "90397942272",
  "regulator": "14.797627462210259573994822111770836749138705",
  "points": [
    [
      "-33",
      "33"
    ],
    [
      "-32",
      "56"
    ],
    [
      "-17",
      "119"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5195: https://elliptic-rank.icarm.cloud/curve/5195. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,6,15,18), 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. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.",
  "created_at": "2026-10-21 09:27:20",
  "updated_at": "2026-10-21 09:27:20"
}