2022-04-06 09:18:19 +0100 commented question compute the equation for elliptic curves from lattices Thank you very much, Max! 2022-04-06 04:21:31 +0100 commented question compute the equation for elliptic curves from lattices Thanks a lot for the anwser ! So there is no program or command in Sage or Pari to do that directly, right? 2022-04-06 04:21:05 +0100 commented question compute the equation for elliptic curves from lattices Thanks a lot for the anwser ! So this no program or command in Sage or Pari to do that, right? 2022-04-06 04:20:03 +0100 commented question compute the equation for elliptic curves from lattices Thanks a lot for the anwser ! 2022-04-05 04:01:25 +0100 commented question compute the equation for elliptic curves from lattices For example, given a basis [1.4752770112052821796 - 0.6182637476411826238i, 1.6774834051116878106 - 2.20502299078472825 2022-04-05 02:55:06 +0100 edited question compute the equation for elliptic curves from lattices compute the equation for elliptic curves from lattices Given a lattice in $\mathbb{C}$, is there commands in Sage or Par 2022-04-05 02:54:29 +0100 commented question compute the equation for elliptic curves from lattices For example, given a basis [0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851i, 0.2 2022-04-05 02:54:13 +0100 commented question compute the equation for elliptic curves from lattices For example, given a basis $[0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851i, 0. 2022-04-05 02:53:54 +0100 commented question compute the equation for elliptic curves from lattices For example, given a basis [0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851i, 0.2 2022-04-05 02:53:16 +0100 commented question compute the equation for elliptic curves from lattices For example, given a basis [0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851I, 0.2 2022-04-03 05:26:10 +0100 edited question compute the equation for elliptic curves from lattices compute the equation for elliptic curves from lattices Given a lattice in$C$, is there commands in Sage or Pari to comp 2022-04-03 05:25:56 +0100 edited question compute the equation for elliptic curves from lattices compute the equation for elliptic curves from lattices Given a lattice in$C$, is there commands in Sage or Pari that co 2022-04-03 05:25:45 +0100 received badge ● Editor (source) 2022-04-03 05:25:45 +0100 edited question compute the equation for elliptic curves from lattices compute the equation for elliptic curves from lattices Given a lattice in$C$, is there command in Sage or Pari that com 2022-04-03 05:25:30 +0100 asked a question compute the equation for elliptic curves from lattices compute the equation for elliptic curves from lattices Given a lattice in$C$, is the command in Sage or Pari that compu 2022-03-27 06:18:37 +0100 commented answer set precision for pari in Sage Thanks a lot ! I find that the .mfsymbol() can set precision in Sage. For example, I use pari.mfsymbol(S,L[0],256) can i 2022-03-24 12:03:13 +0100 commented answer set precision for pari in Sage Thanks a lot ! But this seem not effect when I use Sage. Please see the example I give in the comment below. 2022-03-24 12:01:35 +0100 commented answer set precision for pari in Sage For example, I run the following code in sage from cypari2 import Pari pari = Pari() print(R) K.=CyclotomicFie 2022-03-24 12:00:40 +0100 commented answer set precision for pari in Sage For example, I run the following code in sage from cypari2 import Pari pari = Pari() print(R) K.=CyclotomicFie 2022-03-24 12:00:02 +0100 commented answer set precision for pari in Sage For example, I run the following code in sage from cypari2 import Pari pari = Pari() print(R) K.=CyclotomicField(3) E=p 2022-03-23 09:48:46 +0100 commented answer set precision for pari in Sage Thanks a lot! I tried this command pari.set_real_precision(), but when I use mfsymboleval, the precision does not chang 2022-03-23 08:37:44 +0100 asked a question set precision for pari in Sage set precision for pari in Sage In the pari program, we can use \pb 256 to set the precision. For the pari in Sage, how t 2022-03-23 08:35:44 +0100 commented answer How to find a CM point with the image in the elliptic curve under modular parametrization given Thank you very much, John. 2022-03-23 08:35:42 +0100 received badge ● Supporter (source) 2022-03-23 08:34:58 +0100 received badge ● Scholar (source) 2020-05-28 17:58:51 +0100 received badge ● Popular Question (source) 2020-05-28 17:58:51 +0100 received badge ● Notable Question (source) 2019-08-11 23:05:54 +0100 asked a question How to find a CM point with the image in the elliptic curve under modular parametrization given everyone! Let$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]{3},4)$under the modular parametrization? Can anyone tell me the answer or how to use sagemath to find it? I use the sagemath code EllipticCurve([0,0,1,0,-61]) phi = EllipticCurve([0,0,1,0,-61]).modular_parametrization() f=phi.power_series(prec = 10000)[1] f.truncate(20000)  to get the parametrization of y coordinate, then I use q=var('q') f(q)= df=diff(f,q) NewtonIt(q)=q-(f/df)(q) xn=e^(2*pi*I*a/20.031) for i in range(1000): xn=N(NewtonIt(xn),digits=2000) print xn  to get the numerical$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? 2017-03-29 01:38:01 +0100 received badge ● Nice Question (source) 2017-03-20 11:33:45 +0100 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 10:22:40 +0100 received badge ● Student (source) 2017-03-19 01:48:48 +0100 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[1][0]%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