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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.<a>=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.<a>=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.

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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?

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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?

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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