{
  "id": 5227,
  "curve_key": "105232176:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2192337",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 55.415039001050786,
  "faltings_height": 2.6861603283957227,
  "conductor": "17089214298912",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "23",
    "89"
  ],
  "discriminant": "674375702551809072192",
  "regulator": "858.867021545397571729520774073057331733652909687",
  "points": [
    [
      "-1449",
      "11592"
    ],
    [
      "-1377",
      "20196"
    ],
    [
      "-801",
      "35244"
    ],
    [
      "-425",
      "29240"
    ],
    [
      "13617",
      "1579572"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (3,7,15,19), 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 following the parametrization search 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 10:36:12",
  "updated_at": "2026-10-21 10:36:12"
}