use {identity,negation}_morphism() throughout

src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

@@ -77,7 +77,7 @@
 from sage.rings.number_field.number_field_base import is_NumberField
 
 from sage.schemes.elliptic_curves.weierstrass_morphism \
-        import WeierstrassIsomorphism, isomorphisms, baseWI
+        import WeierstrassIsomorphism, isomorphisms, baseWI, negation_morphism
 
 from sage.sets.set import Set
 
@@ -1272,9 +1272,7 @@ def __neg__(self):
 
         """
         output = copy(self)
-        E2 = output.__E2
-        iso = WeierstrassIsomorphism(E2, (-1,0,-E2.a1(),-E2.a3()))
-        output._set_post_isomorphism(iso)
+        output._set_post_isomorphism(negation_morphism(output.__E2))
         return output
 
     #
@@ -1345,8 +1343,8 @@ def __clear_cached_values(self):
             sage: E = EllipticCurve(QQ, [0,0,0,1,0])
             sage: phi = EllipticCurveIsogeny(E, x)
             sage: old_ratl_maps = phi.rational_maps()
-            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism
-            sage: phi.set_post_isomorphism(WeierstrassIsomorphism(phi.codomain(), (-1,0,0,0)))
+            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import negation_morphism
+            sage: phi.set_post_isomorphism(negation_morphism(phi.codomain()))
             ...
             sage: old_ratl_maps == phi.rational_maps()
             False
@@ -3218,7 +3216,7 @@ def switch_sign(self):
         from sage.misc.superseded import deprecation
         deprecation(32388, 'Elliptic-curve isogenies will be immutable in a future release of Sage.'
                           ' Use -phi instead of phi.switch_sign() to obtain the negated isogeny.')
-        self._set_post_isomorphism(WeierstrassIsomorphism(self.__E2, (-1,0,-self.__E2.a1(),-self.__E2.a3())))
+        self._set_post_isomorphism(negation_morphism(self.__E2))
 
     def dual(self):
         r"""

src/sage/schemes/elliptic_curves/hom.py

@@ -126,11 +126,11 @@ def _richcmp_(self, other, op):
 
         ::
 
-            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism
+            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism, identity_morphism
             sage: E = EllipticCurve([9,9])
             sage: F = E.change_ring(GF(71))
-            sage: wE = WeierstrassIsomorphism(E, (1,0,0,0))
-            sage: wF = WeierstrassIsomorphism(F, (1,0,0,0))
+            sage: wE = identity_morphism(E)
+            sage: wF = identity_morphism(F)
             sage: mE = E.multiplication_by_m_isogeny(1)
             sage: mF = F.multiplication_by_m_isogeny(1)
             sage: [mE == wE, mF == wF]

src/sage/schemes/elliptic_curves/hom_composite.py

@@ -93,7 +93,7 @@
 from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
 from sage.schemes.elliptic_curves.hom import EllipticCurveHom
 from sage.schemes.elliptic_curves.ell_curve_isogeny import EllipticCurveIsogeny
-from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism
+from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism, identity_morphism
 
 from sage.misc.superseded import experimental_warning
 experimental_warning(32744, 'EllipticCurveHom_composite is experimental code.')
@@ -266,7 +266,7 @@ def __init__(self, E, kernel, codomain=None):
         self._phis = _compute_factored_isogeny(kernel)
 
         if not self._phis:
-            self._phis = [WeierstrassIsomorphism(E, (1,0,0,0))]
+            self._phis = [identity_morphism(E)]
 
         if codomain is not None:
             if not isinstance(codomain, EllipticCurve_generic):
@@ -362,7 +362,7 @@ def from_factors(cls, maps, E=None, strict=True):
             E = phi.codomain()
 
         if not maps:
-            maps = (WeierstrassIsomorphism(E, (1,0,0,0)),)
+            maps = (identity_morphism(E),)
 
         if len(maps) == 1 and not strict:
             return maps[0]

src/sage/schemes/elliptic_curves/hom_scalar.py

@@ -306,10 +306,10 @@ def _richcmp_(self, other, op):
 
         TESTS:
 
-            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism
+            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import negation_morphism
             sage: from sage.schemes.elliptic_curves.hom_composite import EllipticCurveHom_composite
             doctest:warning ...
-            sage: neg = WeierstrassIsomorphism(E, [-1,0,0,0])
+            sage: neg = negation_morphism(E)
             sage: neg_psi = EllipticCurveHom_composite.from_factors([psi,neg])
             sage: psi_neg = EllipticCurveHom_composite.from_factors([neg,psi])
             sage: phi == neg_psi == psi_neg == -psi

src/sage/schemes/elliptic_curves/weierstrass_morphism.py

@@ -870,10 +870,10 @@ def __neg__(self):
 
         ::
 
-            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism
+            sage: from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism, identity_morphism
             sage: E = EllipticCurve(QuadraticField(-1), [1,0])
             sage: t = WeierstrassIsomorphism(E, (i,0,0,0))
-            sage: -t^2 == WeierstrassIsomorphism(E, (1,0,0,0))
+            sage: -t^2 == identity_morphism(E)
             True
         """
         a1,_,a3,_,_ = self._domain.a_invariants()
@@ -882,6 +882,23 @@ def __neg__(self):
         return WeierstrassIsomorphism(self._domain, urst, self._codomain)
 
 
+def identity_morphism(E):
+    r"""
+    Given an elliptic curve `E`, return the identity morphism
+    on `E` as a :class:`WeierstrassIsomorphism`.
+
+    EXAMPLES::
+
+        sage: from sage.schemes.elliptic_curves.weierstrass_morphism import identity_morphism
+        sage: E = EllipticCurve([5,6,7,8,9])
+        sage: id_ = identity_morphism(E)
+        sage: id_.rational_maps()
+        (x, y)
+    """
+    R = E.base_ring()
+    zero = R.zero()
+    return WeierstrassIsomorphism(E, (R.one(), zero, zero, zero))
+
 def negation_morphism(E):
     r"""
     Given an elliptic curve `E`, return the negation endomorphism
@@ -895,6 +912,6 @@ def negation_morphism(E):
         sage: neg.rational_maps()
         (x, -5*x - y - 7)
     """
-    a1,_,a3,_,_ = E.a_invariants()
-    return WeierstrassIsomorphism(E, (-1, 0, -a1, -a3))
+    R = E.base_ring()
+    return WeierstrassIsomorphism(E, (-R.one(), R.zero(), -E.a1(), -E.a3()))