diff --git a/jwt/algorithms.py b/jwt/algorithms.py
index 9be50b20..9fbdebb7 100644
--- a/jwt/algorithms.py
+++ b/jwt/algorithms.py
@@ -581,13 +581,20 @@ def to_jwk(key_obj: AllowedECKeys, as_dict: bool = False) -> JWKDict | str:
             obj: dict[str, Any] = {
                 "kty": "EC",
                 "crv": crv,
-                "x": to_base64url_uint(public_numbers.x).decode(),
-                "y": to_base64url_uint(public_numbers.y).decode(),
+                "x": to_base64url_uint(
+                    public_numbers.x,
+                    bit_length=key_obj.curve.key_size,
+                ).decode(),
+                "y": to_base64url_uint(
+                    public_numbers.y,
+                    bit_length=key_obj.curve.key_size,
+                ).decode(),
             }
 
             if isinstance(key_obj, EllipticCurvePrivateKey):
                 obj["d"] = to_base64url_uint(
-                    key_obj.private_numbers().private_value
+                    key_obj.private_numbers().private_value,
+                    bit_length=key_obj.curve.key_size,
                 ).decode()
 
             if as_dict:
diff --git a/jwt/utils.py b/jwt/utils.py
index d469139b..632f88b4 100644
--- a/jwt/utils.py
+++ b/jwt/utils.py
@@ -37,11 +37,11 @@ def base64url_encode(input: bytes) -> bytes:
     return base64.urlsafe_b64encode(input).replace(b"=", b"")
 
 
-def to_base64url_uint(val: int) -> bytes:
+def to_base64url_uint(val: int, *, bit_length: int | None = None) -> bytes:
     if val < 0:
         raise ValueError("Must be a positive integer")
 
-    int_bytes = bytes_from_int(val)
+    int_bytes = bytes_from_int(val, bit_length=bit_length)
 
     if len(int_bytes) == 0:
         int_bytes = b"\x00"
@@ -63,13 +63,10 @@ def bytes_to_number(string: bytes) -> int:
     return int(binascii.b2a_hex(string), 16)
 
 
-def bytes_from_int(val: int) -> bytes:
-    remaining = val
-    byte_length = 0
-
-    while remaining != 0:
-        remaining >>= 8
-        byte_length += 1
+def bytes_from_int(val: int, *, bit_length: int | None = None) -> bytes:
+    if bit_length is None:
+        bit_length = val.bit_length()
+    byte_length = (bit_length + 7) // 8
 
     return val.to_bytes(byte_length, "big", signed=False)