2019-08-11 16:05:54 -0500 asked a question How to find a CM point with the image in the elliptic curve under modular parametrization given everyone! Let $E:y^2+y=x^3-61$ be the minimal model of the elliptic curve 243b. How can I find the CM point $\tau$ in $X_0(243)$ such that $\tau$ maps to the point $(3\sqrt{3},4)$ under the modular parametrization? Can anyone tell me the answer or how to use sagemath to find it? I use the sagemath code EllipticCurve([0,0,1,0,-61]) phi = EllipticCurve([0,0,1,0,-61]).modular_parametrization() f=phi.power_series(prec = 10000) f.truncate(20000)  to get the parametrization of y coordinate, then I use q=var('q') f(q)= df=diff(f,q) NewtonIt(q)=q-(f/df)(q) xn=e^(2*pi*I*a/20.031) for i in range(1000): xn=N(NewtonIt(xn),digits=2000) print xn  to get the numerical $e^{2\pi i \tau}$. After taking log and dividing by $2 \pi i$, I get the numerical $\tau$. But if I use z= p=z.algebraic_dependency(100)  I get the wrong polynomial. Why? 2017-03-28 18:38:01 -0500 received badge ● Nice Question (source) 2017-03-20 05:33:45 -0500 commented answer How to use many cpus to compute in sage Thank you very much! I modified the code into following @parallel(ncpus=47) def P(i,j): if sqrt(i*i+i*j+j*j) in QQ: for k in [0,1,2]: L=Q(i,j)*W*Q(i,j)^(-1)*W^(-1)*B^k if Gamma(L): for l in [0,1,2]: M=Q(i,j)*B*Q(i,j)^(-1)*B^l if Gamma(M): return i,j  I=[1..1000] for i,j in itertools.product([1..100],I): P(i,j) but seems no effect. What is the reason? 2017-03-19 04:22:40 -0500 received badge ● Student (source) 2017-03-18 19:48:48 -0500 asked a question How to use many cpus to compute in sage There is an server with 48 cpus in my office. I want to use all of them to compute the following codes in sage. How can I do that? %time import itertools def is_matrix_integral(M): for i,j in itertools.product(range(2),range(2)): if M[i][j] not in ZZ: return False return True def Gamma(M): if is_matrix_integral(M) and M%243==0 and M.det()==1: return True return False p=4 T=Matrix([[2,-1],[9,-4]])*Matrix([[4,0],[0,9]]) W=Matrix([[0,1],[-243,0]]) S=Matrix([[1,1/3],[0,1]]) A=Matrix([[1,0],[81,1]]) B=-1/(243)*W*A^(-1)*W*A C=Matrix([[1,1/9],[-27,-2]]) e=Matrix([[1,0],[0,-1]]) def Q(a,c): return T*Matrix([[a,a+c],[c,-a]])*T^(-1)*e I=[-100000..-1]+[1..100000] for i,j in itertools.product([1..100000],I): if sqrt(i*i+i*j+j*j) in QQ: for k in [0,1,2]: L=Q(i,j)*W*Q(i,j)^(-1)*W^(-1)*B^k if Gamma(L): print x,Q(i,j),Q(i,j).det(),i,j for l in [0,1,2]: M=Q(i,j)*B*Q(i,j)^(-1)*B^l if Gamma(M): print x,x,M,M.det(),i,j,k,l break