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| author | Sebastiano Tronto <sebastiano@tronto.net> | 2026-06-14 09:58:21 +0200 |
|---|---|---|
| committer | Sebastiano Tronto <sebastiano@tronto.net> | 2026-06-14 09:58:21 +0200 |
| commit | 5ea79c7ae0d44686f1df05c4a016652afbe58968 (patch) | |
| tree | 05f6a052373f5fe0942777a48303b2f8b884cbe1 /l-multiples_l-torsion/test9.gp | |
| download | kummer-notes-code-5ea79c7ae0d44686f1df05c4a016652afbe58968.tar.gz kummer-notes-code-5ea79c7ae0d44686f1df05c4a016652afbe58968.zip | |
Initial commit
Diffstat (limited to 'l-multiples_l-torsion/test9.gp')
| -rwxr-xr-x | l-multiples_l-torsion/test9.gp | 34 |
1 files changed, 34 insertions, 0 deletions
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 | |||
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| 1 | /* Candidate counterex mod3 not surj, unexpected density, rank >=1 */ | ||
| 2 | label = [ "220a3", "220a4", "660c3", "660c4", "770f3", "770f4" ]; | ||
| 3 | |||
| 4 | { | ||
| 5 | for( i = 1, length( data ), | ||
| 6 | print( "Testing curve ", i, ", label ", label[i] ); | ||
| 7 | E = ellinit( label[i] ); | ||
| 8 | f9 = elldivpol( E, 9 ); /* 3-division polynomial */ | ||
| 9 | eqn = y^2 + E[1]*x*y + E[3]*y - x^3 - E[2]*x^2 - E[4]*x - E[5]; /* eqn of E */ | ||
| 10 | res = substpol( polresultant( f9, eqn ), y, x ); /* Keep x for consistency */ | ||
| 11 | print( "Computing K9..." ); | ||
| 12 | K9 = nfinit( nfsplitting( res, 3^5*2 ) ); /* mo3 is at most 6 */ | ||
| 13 | print( "Computed!" ); | ||
| 14 | E_ext = ellinit( E[1..5], K9 ); | ||
| 15 | Egens = ellgenerators(E); | ||
| 16 | for( j = 1, length( Egens ), | ||
| 17 | P = Egens[j]; | ||
| 18 | if( ellisdivisible( substpol(E_ext,x,y), P, 3, &Q ), | ||
| 19 | print( "Found EC ", cremona_label, " with point ", P, | ||
| 20 | " and 3-division point ", Q, " over K9" ); | ||
| 21 | /* Check for 3-divisibility up to torsion */ | ||
| 22 | /* T = elltors(E)[3][1]; | ||
| 23 | if( ellisdivisible( E, elladd(E,P,T), 3 ), | ||
| 24 | print( "P+T_1 is 3-divisible!" ); | ||
| 25 | ); | ||
| 26 | T = ellmul(E,T,2); | ||
| 27 | if( ellisdivisible( E, elladd(E,P,T), 3 ), | ||
| 28 | print( "P+T_2 is 3-divisible!" ); | ||
| 29 | ); */ | ||
| 30 | ); | ||
| 31 | ); | ||
| 32 | ); | ||
| 33 | } | ||
| 34 | |||
