Ticket #14476: trac_14476_bugs_in_local_data.patch

sage/schemes/elliptic_curves/ell_number_field.py

@@ -594 +594 @@
             sage: E = EllipticCurve([25105/216*v - 3839/36, 634768555/7776*v - 98002625/1296, 634768555/7776*v - 98002625/1296, 0, 0])
             sage: E.global_integral_model()
             Elliptic Curve defined by y^2 + (33872485050625*v-31078224284250)*x*y + (2020602604156076340058146664245468750000*v-1871778534673615560803175189398437500000)*y = x^3 + (6933305282258321342920781250*v-6422644400723486559914062500)*x^2 over Number Field in v with defining polynomial x^2 + 161*x - 150
+
+        trac #14476::
+
+            sage: R.<t> = QQ[]
+            sage: K.<g> = NumberField(t^4 - t^3 - 3*t^2 - t + 1)
+            sage: E = EllipticCurve([ -43/625*g^3 + 14/625*g^2 - 4/625*g + 706/625, -4862/78125*g^3 - 4074/78125*g^2 - 711/78125*g + 10304/78125,  -4862/78125*g^3 - 4074/78125*g^2 - 711/78125*g + 10304/78125, 0,0])
+            sage: E.global_integral_model()
+            Elliptic Curve defined by y^2 + (-18*g^3+29*g^2+63*g+7)*x*y + (-704472*g^3-958584*g^2-166242*g+298101)*y = x^3 + (-2859*g^3-3978*g^2-669*g+1332)*x^2 over Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
+
         """
         K = self.base_field()
         ai = self.a_invariants()
-        for a in ai:
-            if not a.is_integral():
-               for P, _ in a.denominator_ideal().factor():
-                   pi = K.uniformizer(P,'positive')
-                   e  = min([(ai[i].valuation(P)/[1,2,3,4,6][i]) for i in range(5)]).floor()
-                   ai = [ai[i]/pi**(e*[1,2,3,4,6][i]) for i in range(5)]
+        Ps = [[ ff[0] for ff in a.denominator_ideal().factor() ] for a in ai if not a.is_integral() ]
+        Ps = sage.misc.misc.union(sage.misc.flatten.flatten(Ps))
+        for P in Ps:
+            pi = K.uniformizer(P,'positive')
+            e  = min([(ai[i].valuation(P)/[1,2,3,4,6][i]) for i in range(5)]).floor()
+            if e < 0 :
+                ai = [ai[i]/pi**(e*[1,2,3,4,6][i]) for i in range(5)]
+            if all(a.is_integral() for a in ai):
+                break
         for z in ai:
             assert z.is_integral(), "bug in global_integral_model: %s" % list(ai)
         return EllipticCurve(list(ai))

sage/schemes/elliptic_curves/ell_local_data.py

@@ -306 +306 @@
 
         INPUT:
 
-        - ``reduce`` -- (default: True) if set to True the EC returned
-          by Tate's algorithm will be
-          "reduced" as specified in _reduce_model() for curves over
-          number fields.
+        - ``reduce`` -- (default: True) if set to True and if the initial
+          elliptic curve had globally integral coefficients, then the
+          elliptic curve returned by Tate's algorithm will be "reduced" as
+          specified in _reduce_model() for curves over number fields.
 
         EXAMPLES::
 
@@ -342 +342 @@
             Elliptic Curve defined by y^2 = x^3 - x^2 - 3*x + 2 over Rational Field
             sage: E.local_data(ZZ.ideal(2), algorithm="pari").minimal_model()
             Elliptic Curve defined by y^2 = x^3 - x^2 - 3*x + 2 over Rational Field
+
+        trac 14476::
+
+            sage: t = QQ['t'].0
+            sage: K.<g> = NumberField(t^4 - t^3-3*t^2 - t +1)
+            sage: E = EllipticCurve([-2*g^3 + 10/3*g^2 + 3*g - 2/3, -11/9*g^3 + 34/9*g^2 - 7/3*g + 4/9, -11/9*g^3 + 34/9*g^2 - 7/3*g + 4/9, 0, 0])
+            sage: vv = K.fractional_ideal(g^2 - g - 2)
+            sage: E.local_data(vv).minimal_model()
+            Elliptic Curve defined by y^2 + (-2*g^3+10/3*g^2+3*g-2/3)*x*y + (-11/9*g^3+34/9*g^2-7/3*g+4/9)*y = x^3 + (-11/9*g^3+34/9*g^2-7/3*g+4/9)*x^2 over Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
+            
         """
         if reduce:
             try:
                 return self._Emin_reduced
             except AttributeError:
                 pass
-            self._Emin_reduced = self._Emin._reduce_model()
-            return self._Emin_reduced
+            # trac 14476 we only reduce if the coefficients are globally integral
+            if all(a.is_integral() for a in self._Emin.a_invariants()):
+                self._Emin_reduced = self._Emin._reduce_model()
+                return self._Emin_reduced
+            else:
+                return self._Emin
         else:
             try:
                 return self._Emin