{
  "id": 1133,
  "curve_key": "113148496:223049299456",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-2357260",
    "-257373158"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "naive_height": 55.632634913596,
  "faltings_height": 2.702173269732632,
  "conductor": "7727548608960",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "113",
    "769",
    "5449"
  ],
  "discriminant": "809515002817537944000",
  "regulator": "26835.837950067874948551723670466578955882219651218",
  "points": [
    [
      "-181",
      "12780"
    ],
    [
      "-321",
      "21590"
    ],
    [
      "-801",
      "-33410"
    ],
    [
      "1659",
      "-19880"
    ],
    [
      "-579/4",
      "71905/8"
    ],
    [
      "1887",
      "-44834"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#16 and mapping all 6 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:37:05",
  "updated_at": "2026-09-23 21:37:05"
}