diff -r 76f8dec0779b -r 0c608bbd5653 sage/rings/qqbar.py
@@ -3276,6 +3276,17 @@
         self.exactify()
         return self._descr.rational_argument(self)

+    def is_square(self):
+        """
+        Returns True as all algebraic numbers are square.
+
+        EXAMPLES::
+
+            sage: QQbar(sqrt(5)).is_square()
+            True
+        """
+        return True
+
 class AlgebraicReal(AlgebraicNumber_base):
     def __init__(self, x):
         AlgebraicNumber_base.__init__(self, AA, x)
diff -r 76f8dec0779b -r 0c608bbd5653 sage/schemes/elliptic_curves/constructor.py
@@ -259,6 +275,9 @@
     elif rings.is_FiniteField(R) or (rings.is_IntegerModRing(R) and R.characteristic().is_prime()):
         return ell_finite_field.EllipticCurve_finite_field(x, y)

+    elif rings.is_Field(R):
+        return ell_field.EllipticCurve_field(x,y)
+
     return ell_generic.EllipticCurve_generic(x, y)