diff --git a/src/sage/rings/polynomial/symmetric_reduction.pyx b/src/sage/rings/polynomial/symmetric_reduction.pyx
index 0559aa77ca8..0da8d656830 100644
--- a/src/sage/rings/polynomial/symmetric_reduction.pyx
+++ b/src/sage/rings/polynomial/symmetric_reduction.pyx
@@ -254,9 +254,9 @@ cdef class SymmetricReductionStrategy:
         return richcmp((left._parent, left._lm, left._tail),
                        (right._parent, right._lm, right._tail), op)
 
-    def gens(self) -> list:
+    def gens(self) -> tuple:
         """
-        Return the list of Infinite Polynomials modulo which ``self`` reduces.
+        Return the tuple of Infinite Polynomials modulo which ``self`` reduces.
 
         EXAMPLES::
 
@@ -269,9 +269,9 @@ cdef class SymmetricReductionStrategy:
                 y_2*y_1^2,
                 y_2^2*y_1
             sage: S.gens()
-            [y_2*y_1^2, y_2^2*y_1]
+            (y_2*y_1^2, y_2^2*y_1)
         """
-        return self._lm
+        return tuple(self._lm)
 
     def setgens(self, L):
         """
diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
index 518fda03481..cafa2eaee3e 100644
--- a/src/sage/schemes/elliptic_curves/ell_number_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
@@ -158,7 +158,7 @@ def base_extend(self, R):
             [(52 : 111 : 1)]
             sage: EK = E.base_extend(K)
             sage: EK.gens()
-            [(52 : 111 : 1)]
+            ((52 : 111 : 1),)
         """
         E = super().base_extend(R)
         if isinstance(E, EllipticCurve_number_field):
@@ -2328,9 +2328,9 @@ def gens(self, **kwds):
             sage: K.<a> = NumberField(x^2 + 23, 'a')
             sage: E = EllipticCurve(K,[0,0,0,101,0])
             sage: E.gens()
-            [(23831509/8669448*a - 2867471/8669448 : 76507317707/18049790736*a - 424166479633/18049790736 : 1),
+            ((23831509/8669448*a - 2867471/8669448 : 76507317707/18049790736*a - 424166479633/18049790736 : 1),
              (-2031032029/969232392*a + 58813561/969232392 : -15575984630401/21336681877488*a + 451041199309/21336681877488 : 1),
-             (-186948623/4656964 : 549438861195/10049728312*a : 1)]
+             (-186948623/4656964 : 549438861195/10049728312*a : 1))
 
         It can happen that no points are found if the height bounds
         used in the search are too small (see :issue:`10745`)::
@@ -2338,11 +2338,11 @@ def gens(self, **kwds):
             sage: K.<t> = NumberField(x^4 + x^2 - 7)
             sage: E = EllipticCurve(K, [1, 0, 5*t^2 + 16, 0, 0])
             sage: E.gens(lim1=1, lim3=1)
-            []
+            ()
             sage: E.rank()
             1
             sage: gg=E.gens(lim3=13); gg  # long time (about 4s)
-            [(... : 1)]
+            ((... : 1),)
 
         Check that the point found has infinite order, and that it is on the curve::
 
@@ -2356,7 +2356,7 @@ def gens(self, **kwds):
             sage: K.<t> = NumberField(x^2 - 17)
             sage: E = EllipticCurve(K, [-4, 0])
             sage: E.gens()
-            [(-1/2*t + 1/2 : -1/2*t + 1/2 : 1), (-t + 3 : -2*t + 10 : 1)]
+            ((-1/2*t + 1/2 : -1/2*t + 1/2 : 1), (-t + 3 : -2*t + 10 : 1))
             sage: E.rank()
             2
 
@@ -2368,7 +2368,7 @@ def gens(self, **kwds):
             sage: EK.rank()
             0
             sage: EK.gens()
-            []
+            ()
 
         IMPLEMENTATION:
 
@@ -2378,10 +2378,10 @@ def gens(self, **kwds):
         PARI/GP scripts from http://www.math.unicaen.fr/~simon/.
         """
         try:
-            return self.gens_quadratic(**kwds)
+            return tuple(self.gens_quadratic(**kwds))
         except ValueError:
             self.simon_two_descent(**kwds)
-            return self._known_points
+            return tuple(self._known_points)
 
     def period_lattice(self, embedding):
         r"""
diff --git a/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py b/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py
index 36d629888b5..23766b59996 100644
--- a/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py
+++ b/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py
@@ -572,7 +572,7 @@ def poly_ring(self):
 
     def gens(self):
         """
-        Return a list [x, T] where x and T are the generators of the ring
+        Return a tuple (x, T) where x and T are the generators of the ring
         (as element *of this ring*).
 
         .. NOTE::