various small code tweaks

src/sage/schemes/elliptic_curves/ell_finite_field.py

@@ -684,23 +684,23 @@ def frobenius_order(self):
 
             sage: E = EllipticCurve(GF(11),[3,3])
             sage: E.frobenius_order()
-            Order of conductor 2 generated by phi
-             in Number Field in phi with defining polynomial x^2 - 4*x + 11
+            Order of conductor 2 generated by pi
+             in Number Field in pi with defining polynomial x^2 - 4*x + 11
 
-        For some supersingular curves, Frobenius is in Z and the Frobenius
-        order is Z::
+        For some supersingular curves, Frobenius is in `\ZZ` and the Frobenius
+        order is `\ZZ`::
 
             sage: # needs sage.rings.finite_rings
             sage: E = EllipticCurve(GF(25,'a'),[0,0,0,0,1])
             sage: R = E.frobenius_order()
             sage: R
             Order generated by []
-             in Number Field in phi with defining polynomial x + 5
+             in Number Field in pi with defining polynomial x + 5
             sage: R.degree()
             1
         """
         f = self.frobenius_polynomial().factor()[0][0]
-        return ZZ.extension(f,names='phi')
+        return ZZ.extension(f, names='pi')
 
     def frobenius(self):
         r"""
@@ -717,7 +717,7 @@ def frobenius(self):
 
             sage: E = EllipticCurve(GF(11),[3,3])
             sage: E.frobenius()
-            phi
+            pi
             sage: E.frobenius().minpoly()
             x^2 - 4*x + 11
 
@@ -1562,28 +1562,28 @@ def height_above_floor(self, ell, e):
         """
         if self.is_supersingular():
             raise ValueError("{} is not ordinary".format(self))
-        if e == 0:
-            return 0
+        if not e:
+            return ZZ.zero()
         j = self.j_invariant()
         if j in [0, 1728]:
             return e
         F = j.parent()
         x = polygen(F)
         from sage.rings.polynomial.polynomial_ring import polygens
         from sage.schemes.elliptic_curves.mod_poly import classical_modular_polynomial
-        X, Y = polygens(F, "X, Y", 2)
+        X, Y = polygens(F, 'X,Y')
         phi = classical_modular_polynomial(ell)(X, Y)
         j1 = phi([x,j]).roots(multiplicities=False)
         nj1 = len(j1)
         on_floor = self.two_torsion_rank() < 2 if ell == 2 else nj1 <= ell
         if on_floor:
-            return 0
+            return ZZ.zero()
         if e == 1 or nj1 != ell+1:  # double roots can only happen at the surface
             return e
         if nj1 < 3:
-            return 0
+            return ZZ.zero()
         j0 = [j,j,j]
-        h = 1
+        h = ZZ.one()
         while True:
             for i in range(3):
                 r = (phi([x,j1[i]])//(x-j0[i])).roots(multiplicities=False)