diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index d2cfb771..eca4c59f 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -12,6 +12,7 @@ Fixed
 
 - Annotate PyJWKSet.keys for pyright by @tamird in `#1134 <https://github.com/jpadilla/pyjwt/pull/1134>`__
 - Close ``HTTPError`` response to prevent ``ResourceWarning`` on Python 3.14 by @veeceey in `#1133 <https://github.com/jpadilla/pyjwt/pull/1133>`__
+- Do not keep ``algorithms`` dict in PyJWK instances by @akx in `#1143 <https://github.com/jpadilla/pyjwt/pull/1143>`__
 
 Added
 ~~~~~
diff --git a/jwt/api_jwk.py b/jwt/api_jwk.py
index 960de75c..4ae7cc3f 100644
--- a/jwt/api_jwk.py
+++ b/jwt/api_jwk.py
@@ -28,7 +28,6 @@ def __init__(self, jwk_data: JWKDict, algorithm: str | None = None) -> None:
         :raises MissingCryptographyError: If the algorithm requires ``cryptography`` to be installed and it is not available.
         :raises PyJWKError: If unable to find an algorithm for the key.
         """
-        self._algorithms = get_default_algorithms()
         self._jwk_data = jwk_data
 
         kty = self._jwk_data.get("kty", None)
@@ -73,10 +72,12 @@ def __init__(self, jwk_data: JWKDict, algorithm: str | None = None) -> None:
 
         self.algorithm_name = algorithm
 
-        if algorithm in self._algorithms:
-            self.Algorithm = self._algorithms[algorithm]
-        else:
-            raise PyJWKError(f"Unable to find an algorithm for key: {self._jwk_data}")
+        try:
+            self.Algorithm = get_default_algorithms()[algorithm]
+        except KeyError:
+            raise PyJWKError(
+                f"Unable to find an algorithm for key: {self._jwk_data}",
+            ) from None
 
         self.key = self.Algorithm.from_jwk(self._jwk_data)