{
  "id": 1146,
  "curve_key": "21253657305362665195216:-581336983706715165344718003708736",
  "ainvs": [
    "0",
    "1",
    "0",
    "-442784527195055524900",
    "672843730994436598972849551548"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "naive_height": 154.23244782577223,
  "faltings_height": 10.918770581644383,
  "conductor": "104034096695931795120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "37",
    "41",
    "137",
    "191",
    "557"
  ],
  "discriminant": "5360362149881188634737018468131213727988787863038447736219040000",
  "regulator": "11348194.14970519083630702006996408532292227619385686",
  "points": [
    [
      "-952815889",
      "1045882805227260"
    ],
    [
      "-9707941426/25",
      "-114886236291804432/125"
    ],
    [
      "27736281086",
      "-3119167261000560"
    ],
    [
      "-18408975874",
      "-1607926722882480"
    ],
    [
      "906093566",
      "521903657418000"
    ],
    [
      "160140179951",
      "-63533774522567580"
    ],
    [
      "185837115232991",
      "-2533370330950967781000"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1089 and mapping all 7 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 21:37:32",
  "updated_at": "2026-09-23 21:37:32"
}