{
  "id": 5093,
  "curve_key": "653616:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-13617",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 40.1708259060974,
  "faltings_height": 1.415809237149607,
  "conductor": "659280672",
  "bad_primes": [
    "2",
    "3",
    "17",
    "89"
  ],
  "discriminant": "161593648391232",
  "regulator": "19.371393622973145695542936912196162683409333",
  "points": [
    [
      "-89",
      "712"
    ],
    [
      "-81",
      "756"
    ],
    [
      "801",
      "22428"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5092: https://elliptic-rank.icarm.cloud/curve/5092. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,9,33,45), 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 02:37:40",
  "updated_at": "2026-10-21 02:37:40"
}