From 5ea79c7ae0d44686f1df05c4a016652afbe58968 Mon Sep 17 00:00:00 2001
From: Sebastiano Tronto <sebastiano@tronto.net>
Date: Sun, 14 Jun 2026 09:58:21 +0200
Subject: Initial commit

---
 l-multiples_l-torsion/test9.gp | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100755 l-multiples_l-torsion/test9.gp

(limited to 'l-multiples_l-torsion/test9.gp')

diff --git a/l-multiples_l-torsion/test9.gp b/l-multiples_l-torsion/test9.gp
new file mode 100755
index 0000000..47b00ab
--- /dev/null
+++ b/l-multiples_l-torsion/test9.gp
@@ -0,0 +1,34 @@
+/* Candidate counterex mod3 not surj, unexpected density, rank >=1 */
+label = [ "220a3", "220a4", "660c3", "660c4", "770f3", "770f4" ];
+
+{
+for( i = 1, length( data ), 
+  print( "Testing curve ", i, ", label ", label[i] );
+  E = ellinit( label[i] );
+  f9 = elldivpol( E, 9 ); /* 3-division polynomial */
+  eqn = y^2 + E[1]*x*y + E[3]*y - x^3 - E[2]*x^2 - E[4]*x - E[5]; /* eqn of E */
+  res = substpol( polresultant( f9, eqn ), y, x ); /* Keep x for consistency */
+  print( "Computing K9..." );
+  K9 = nfinit( nfsplitting( res, 3^5*2 ) ); /* mo3 is at most 6 */
+  print( "Computed!" );
+  E_ext = ellinit( E[1..5], K9 );
+  Egens = ellgenerators(E);
+  for( j = 1, length( Egens ), 
+    P = Egens[j];
+    if( ellisdivisible( substpol(E_ext,x,y), P, 3, &Q ),
+      print( "Found EC ", cremona_label, " with point ", P, 
+             " and 3-division point ", Q, " over K9" );
+      /* Check for 3-divisibility up to torsion */
+      /* T = elltors(E)[3][1];
+      if( ellisdivisible( E, elladd(E,P,T), 3 ),
+        print( "P+T_1 is 3-divisible!" );
+      );
+      T = ellmul(E,T,2);    
+      if( ellisdivisible( E, elladd(E,P,T), 3 ),
+        print( "P+T_2 is 3-divisible!" );
+      ); */ 
+    );
+  );
+);
+}
+
-- 
cgit v1.3