Sorry the file got truncated. basic commands e=ellinit([0,0,0,a,b]) (Initializes curve, remember to use Mods for a and b) ellisoncurve(e,P) (checks if P is on e) ellpow(e,P,n) (computes nP) elladd(e,P,Q) (adds P and Q) ellap(e,p) (computes t such that #E = p+1-t) ? for(x=0,p-1,if(kronecker(x^3+lift(a)*x+lift(b),p)==1,print(x);break)) 0 ? sqrt(b) %25 = Mod(1968387009, 10000000019) ? P=[0,%25] %26 = [0, Mod(1968387009, 10000000019)] ? ellisoncurve(e,P) %27 = 1 ? ellpow(e,P,3) %28 = [Mod(54599374, 10000000019), Mod(7346422527, 10000000019)] ? for(n=1,2*p,if(ellpow(e,P,n)==[0],print(n))) ^C *** ellpow: user interrupt after 34,050 ms. ? factor(p+1-%20) %29 = [2 1] [15427 1] [324101 1] ? ellpow(e,P,2) %30 = [Mod(1797458710, 10000000019), Mod(1711160604, 10000000019)] ? ellpow(e,P,15427) %31 = [Mod(3515563503, 10000000019), Mod(703907807, 10000000019)] ? ellpow(e,P,324101) %32 = [Mod(6003584693, 10000000019), Mod(8549519529, 10000000019)] ? ellpow(e,P,324101*2) %33 = [Mod(6566839396, 10000000019), Mod(2735501833, 10000000019)] ? ellpow(e,P,324101*2*15427) %34 = [0] ? ellpow(e,P,2*15427) %35 = [Mod(9473185289, 10000000019), Mod(7406587460, 10000000019)] ? ellpow(e,P,324101*15427) %36 = [0] ?