do(e)=elltors(ellinit(e));
do([0, -1, 1, -7820, -263580])
do([1, 0, 1, -171, -874])
do([0, 1, 1, -9, -15])
do([1, 1, 1, -80, 242])
do([0, -1, 1, -10, -20])
do([1, 0, 1, 4, -6])
do([1, -1, 1, -3, 3])
do([1, 1, 1, 35, -28])
do([1, -1, 1, -14, 29])
do([1, 0, 0, -45, 81])
do([1, -1, 1, -122, 1721])

do([1, 1, 1, -135, -660])
do([1, 1, 1, -10, -10])
do([1, 0, 1, -19, 26])
do([1, 0, 0, -1070, 7812])
do([1,0,0,-372368141774940800,87459461608665181808640000])
do([0,706607569223786457,0,-1866575649655837263252847197205171425,-1298198297451307472292414787720779720378300792679274425])

K=nfinit(t^2-5);
s=Mod(t,K.pol);
E=ellinit([-31/60*s-1/12, -11/9*s-8/3, -11/9*s-8/3, 0, 0], K);
T=elltors(E)
ellorder(E,T.gen[1])
ellorder(E,T.gen[2])

K=nfinit(t^4+18*t^2-324*t-27);E=ellinit([1,3],K);
elltors(E)

do(v,K)=
{
  my(e=ellinit(v,K), t=elltors(e));
  if (apply(p->ellorder(e,p),t.gen) != t.cyc, error(v));
  t;
}


K=nfinit(t^8-998*t^6+44424*t^4+5106934*t^2+126046063);
do([1,3],K)

K=nfinit(polcyclo(11,t));
do([0,-1,1,0,0],K)

\\ [11]
K = nfinit(y^2+7);
a1=-209*y-579;
a2=26752*y+147840;
a3=-10486784*y-57953280;
do([a1,a2,a3,0,0],K)

\\ [15]
a1=(-2*y+15);
a2=26*y-14;
a3=26*y-14;
do([a1,a2,a3,0,0],K)

\\ [10,2]
a2=-261214369/131072;
a4=75626226572068161/68719476736;
K=nfinit(y^2+2);
do([0,a2,0,a4,0],K)

\\ [12,2]
K=nfinit(y^2-13);
a2=(-4289032*y+15673889)/65536
a4=(-32028469200*y+115490749725)/4194304
do([0,a2,0,a4,0],K)

\\ [14]
K=nfinit(y^2+11);
a1=-2601888534886283704*y+154252733407512581857;
a2=-313766195076761969526071169866614175160*y+1735663223649526033628839600302712469280
a3=-43286504429925775681153399339981518914403432663035092419000*y+239448337641930912934754848966237361950084593095601008052000;
do([a1,a2,a3,0,0],K)

\\ [16,2]
K=nfinit(y^4+2002*y^2+116281);
a2=12974641/13176900;
a4=16/14641;
do([0,a2,0,a4,0],K)

\\ [3,3]
K=nfinit(y^2+3);
do([1,-1,0,12,8],K)

\\ [20]
K=nfinit(y^3-y^2-2*y-2);
a=(-5*y^2-y)/2;
b=-14*y^2-12*y-8;
do([a,b,b,0,0],K)

\\ [6,6]
K=nfinit(y^4+5*y^2+1);
a=9/8;
b=7/64;
do([a,b,b,0,0],K)

\\ [8,4]
K=nfinit(y^4+541*y^2+72900);
a=431/690;
b=-259/529;
do([a,b,b,0,0],K)

\\ [8,8]
K=nfinit(y^16-8*y^15+36*y^14-104*y^13+220*y^12-368*y^11+516*y^10-624*y^9+664*y^8-624*y^7+516*y^6-368*y^5+220*y^4-104*y^3+36*y^2-8*y+1);
do([-1,0],K)

\\ [9,3]
K=nfinit(x^6+3);
do([1,-1,1,-14,29],K)

E = ellinit([-2147484185^2,0]);
elltors(E)
ellorder(E, [0,0])
ellorder(E, [2147484185, 0])
ellorder(E, [2147484185/3, 1/11])
E = ellinit([1,1]); P = [72, 611];
ellorder (E, ellmul(E, P, 20))

\\#1660
do([2,x],nfinit(x^2+2))

\\#1920
E=ellinit([0,1,1,-1805632198953220354072743054330,937164323059943920996847199260009653476285734]);
elltors(E)
