diff --git a/src/sage/rings/rational.pyx b/src/sage/rings/rational.pyx
index b1acb90b174..5bff1754afb 100644
--- a/src/sage/rings/rational.pyx
+++ b/src/sage/rings/rational.pyx
@@ -3979,6 +3979,18 @@ cdef class Z_to_Q(Morphism):
         from sage.categories.sets_with_partial_maps import SetsWithPartialMaps
         return Q_to_Z(self._codomain.Hom(self.domain(), category=SetsWithPartialMaps()))
 
+    def is_surjective(self):
+        r"""
+        Return whether this morphism is surjective.
+
+        EXAMPLES::
+
+            sage: QQ.coerce_map_from(ZZ).is_surjective()
+            False
+
+        """
+        return False
+
 cdef class Q_to_Z(Map):
     r"""
     A morphism from `\QQ` to `\ZZ`.