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read("bunch_of_curves.gp");
{
for( i = 1, length( data ),
print( "Testing curve with coefficients ", data[i] );
E = ellinit( data[i] );
f4 = elldivpol( E, 4 ); /* 4-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( f4, eqn ), y, x ); /* Keep x for consistency */
print( "Computing K4..." );
K4 = nfinit( nfsplitting( res, 96 ) );
print( "Computed!" );
E_ext = ellinit( E[1..5], K4 );
Egens = ellgenerators(E);
for( j = 1, length( Egens ),
P = Egens[j];
if( ellisdivisible( substpol(E_ext,x,y), P, 2, &Q ),
print( "Found EC ", cremona_label, " with point ", P,
" and 2-division point ", Q, " over K4" );
if( ellisdivisible( substpol(E_ext,x,y), P, 4, &Q ),
print( "Even 4-divisible! 4-division point: ", Q );
);
/* 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!" );
); */
);
);
);
}
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