Fix bug with pari interface in classical_modular_polynomial

Author: drago-96

src/sage/schemes/elliptic_curves/mod_poly.py

@@ -87,6 +87,21 @@ def classical_modular_polynomial(l, j=None):
         sage: Y = polygen(parent(j), 'Y')
         sage: classical_modular_polynomial(l,j) == classical_modular_polynomial(l)(j,Y)
         True
+        sage: p = 2^216 * 3^137 - 1
+        sage: F.<i> = GF(p^2, modulus=[1,0,1])
+        sage: l = random_prime(50)
+        sage: j = F.random_element()
+        sage: Y = polygen(parent(j), 'Y')
+        sage: classical_modular_polynomial(l,j) == classical_modular_polynomial(l)(j,Y)
+        True
+        sage: E = EllipticCurve(F, [0, 6, 0, 1, 0])
+        sage: j = E.j_invariant()
+        sage: classical_modular_polynomial(l,j) == classical_modular_polynomial(l)(j,Y)
+        True
+        sage: R.<Y> = QQ['Y']
+        sage: j = QQ(1/2)
+        sage: classical_modular_polynomial(l, j) == classical_modular_polynomial(l)(j, Y)
+        True
     """
     l = ZZ(l)
 
@@ -114,7 +129,8 @@ def classical_modular_polynomial(l, j=None):
 
         return Phi
 
-    R = parent(j)['Y']
+    Rb = j.parent()
+    R = Rb['Y']
     Y = R.gen()
 
     # If the generic polynomial is in the cache or the database, evaluating
@@ -133,12 +149,19 @@ def classical_modular_polynomial(l, j=None):
     # Now try to get the instantiated modular polynomial directly from PARI.
     # This should be slightly more efficient (in particular regarding memory
     # usage) than computing and evaluating the generic modular polynomial.
-    try:
-        pari_Phi = pari.polmodular(l, 0, j)
-    except PariError:
-        pass
-    else:
-        return R(pari_Phi)
+    # This currently only works if we are over Z/nZ.
+    n = Rb.characteristic()
+    if n > 0:
+        from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+        try:
+            jn = IntegerModRing(n)(j)
+            pari_Phi = pari.polmodular(l, 0, jn)
+        except TypeError:
+            pass
+        except PariError:
+            pass
+        else:
+            return R(pari_Phi)
 
     # Nothing worked. Fall back to computing the generic modular polynomial
     # and simply evaluating it.