{{{id=1|
var('x')
K.<a>=NumberField(x^2-x-1)
import nosqlite
db=nosqlite.Client('/home/psharaba/table/ECdb').db
from psage.ellcurve.minmodel.sqrt5 import canonical_model
///
}}}

{{{id=10|
from nosqlite import Client

def local_db():
    return Client(DATA+'localdb').db

def network_db():    
    raise NotImplementedError

def create_local_db():
    db = local_db()
    c = db.curves  # collection
    c.ensure_index(unique=True, weq=1)
    for X in open('/home/psharaba/table/CLlist.txt').readlines():
        v = X.split()
        E=EllipticCurve(K,eval(v[2]))
        E=canonical_model(E.global_minimal_model())
        
        d = {'N':int(v[0]),
             'cond':v[1],
             'weq':str(E)}
        c.insert(d)
///
}}}

{{{id=11|
create_local_db()
///
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_27.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Y3JlYXRlX2xvY2FsX2RiKCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpFxBvHn/___code___.py", line 2, in <module>
    exec compile(u'create_local_db()' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpFzqZMs/___code___.py", line 23, in create_local_db
    c.insert(d)
  File "/home/wstein/nosqlite/nosqlite.py", line 845, in insert
    self.database(_insert_statement(self.name, d.keys(), on_conflict), d.values(), coerce=coerce)
  File "/home/wstein/nosqlite/nosqlite.py", line 592, in __call__
    return self.client(cmds, t, file=self.name, many=many, coerce=coerce)
  File "/home/wstein/nosqlite/nosqlite.py", line 467, in __call__
    return self.server.execute(cmd, t, file, many)
  File "/home/wstein/nosqlite/nosqlite.py", line 348, in execute
    o = cursor.executemany(*c) if many else cursor.execute(*c)
sqlite3.IntegrityError: column weq is not unique
}}}

{{{id=3|
X=db("select ainv1 from N1k WHERE found='CL' ORDER BY N,eta")
///
}}}

{{{id=4|
c
///
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_20.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Yw=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpOJbqPT/___code___.py", line 2, in <module>
    exec compile(u'c' + '\n', '', 'single')
  File "", line 1, in <module>
    
NameError: name 'c' is not defined
}}}

{{{id=8|
test=[]
///
}}}

{{{id=20|
E=EllipticCurve(K,[a,a,a+1,19*a-24,-13*a+21])
///
}}}

{{{id=21|
E.conductor().norm()
///
84609727705
}}}

{{{id=22|
X=db("select ainv1 from N1k WHERE Lstar=100 ORDER BY N,eta")
X[0]
print type(eval(X[0][0]))
///
<type 'list'>
}}}

{{{id=2|
c = db.N1k
X=db('select ainv1 from N1k WHERE Lstar=100 ORDER BY N,eta')
@parallel(8)
def comp(ainv):
    E=EllipticCurve(K,eval(ainv))
    E=canonical_model(E.global_minimal_model())
    F=EllipticCurve(K,list(E.short_weierstrass_model().a_invariants()))    
    v=F.lseries().dokchitser()
    f=v.taylor_series(1,6)
    r_an=0
    while abs(f[r_an])<1e-10:
        r_an += 1
        if r_an == 6:
            raise RuntimeError
    Lstar=float(f[r_an])
    d = {'Lstar':Lstar} 
    c.update(d, ainv1=ainv)
    print d
    
for s in range(len(X)):
    A=X[s][0]
    comp(A)    
    print A
///
{'Lstar': 1.6601602274532463}
[a+1,-a,a,4*a-8,6*a-11]
{'Lstar': 1.2663734650443368}
[0,0,0,-a+1,a-2]
{'Lstar': 1.4423431483767097}
[1,1,0,4*a-7,7*a-12]
{'Lstar': 1.40058926314229}
[a,1,1,6*a-9,-6*a+10]
{'Lstar': 1.4690761070275693}
[a+1,-a+1,a+1,3*a-8,-4*a+5]
{'Lstar': 0.92996118822906293}
[a+1,0,a+1,9*a-17,-19*a+29]
}}}

{{{id=24|
7 curves left to find Lstar
///
}}}

{{{id=27|
db.N1k.columns()
///
[u'rhi', u'ordD', u'cond1', u'ainv2', u'ainv1', u'cond2', u'tor', u'tama', u'kod', u'sign', u'rlow', u'eta', u'found', u'N', u'ordj', u'nh', u'Lstar', u'fh', u'mtrx', u'label']
}}}

{{{id=9|
test=db("select N,eta,ainv1,Lstar,found from N1k ORDER BY N,eta,Lstar")
///
}}}

{{{id=19|
test2=[]
for t in range(len(test)):
    if type(test[t][3]) != type(float(2)):
        print test[t][2],test[t][3],test[t][4]
///
}}}

{{{id=28|
list(db.N1k.find('N=836'))
///
[{u'nh': 39.506714554756989, u'rlow': 1, u'tama': u'2,1,1', u'cond1': u'-2*a-28', u'ainv2': u'[a,0,a+1,-a,0]', u'ainv1': u'[a+1,-a,a,-a,-a+1]', u'cond2': u'2*a-30', u'tor': 1, u'Lstar': 1.27875348749, u'ordD': u'2,1,1', u'kod': u'I2,I1,I1', u'sign': u'-,-', u'rhi': 1, u'eta': 1692, u'label': u'836a2a', u'fh': -0.93545108014062595, u'found': u'J', u'N': 836, u'mtrx': u'matrix(1,[0])', u'ordj': u'2,1,1'}, {u'nh': 41.836555066281122, u'rlow': 0, u'tama': u'1,1,1', u'cond1': u'-2*a-28', u'ainv2': u'[a+1,-a,1,-1,0]', u'ainv1': u'[a,0,1,-a,0]', u'cond2': u'2*a-30', u'tor': 3, u'Lstar': 1.5108562088699999, u'ordD': u'1,1,1', u'kod': u'I1,I1,I1', u'sign': u'-,-', u'rhi': 0, u'eta': 1692, u'label': u'836a3a', u'fh': -1.0227461202109687, u'found': u'J', u'N': 836, u'mtrx': u'matrix(3,[0,3,0,3,0,3,0,3,0])', u'ordj': u'1,1,1'}, {u'nh': 53.356844089872212, u'rlow': 0, u'tama': u'1,3,3', u'cond1': u'-2*a-28', u'ainv2': u'[a+1,-a,1,-5*a+4,-2*a-4]', u'ainv1': u'[a,0,1,4*a,2*a-6]', u'cond2': u'2*a-30', u'tor': 3, u'Lstar': 1.5108562088745863, u'ordD': u'3,3,3', u'kod': u'I3,I3,I3', u'sign': u'-,-', u'rhi': 0, u'eta': 1692, u'label': u'836a1a', u'fh': -0.47343997587691361, u'found': u'CL', u'N': 836, u'ordj': u'3,3,3'}, {u'rlow': 0, u'tama': u'1,3,3', u'cond1': u'-2*a-28', u'ainv2': u'[a+1,a+1,a+1,-18*a-4,-11*a-10]', u'ainv1': u'[a,a,a+1,19*a-24,-13*a+21]', u'cond2': u'2*a-30', u'tor': 3, u'Lstar': u'REMOVE THIS CURVE', u'ordD': u'3,3,3', u'kod': u'I3,I3,I3', u'sign': u'-,-', u'rhi': 0, u'eta': 1692, u'label': u'836a1b', u'found': u'CL', u'N': 836, u'ordj': u'3,3,3'}, {u'rlow': 1, u'tama': u'3,1,2', u'cond1': u'26*a-10', u'ainv2': u'[1,a,0,-3*a-4,-7*a-3]', u'ainv1': u'[1,-a+1,0,3*a-7,7*a-10]', u'cond2': u'-26*a+16', u'tor': 2, u'Lstar': 1.3043748959826422, u'ordD': u'3,1,4', u'kod': u'I3,I1,I4', u'sign': u'+,+', u'rhi': 1, u'eta': 1708, u'label': u'836b1a', u'found': u'J', u'N': 836, u'ordj': u'3,1,4'}, {u'nh': 77.013517221962417, u'rlow': 0, u'tama': u'1,1,1', u'cond1': u'-2*a-28', u'ainv2': u'[a+1,-a,1,-105*a-206,-946*a-1272]', u'ainv1': u'[a,0,1,104*a-310,946*a-2218]', u'cond2': u'2*a-30', u'tor': 1, u'Lstar': 1.5108562088699999, u'ordD': u'9,1,1', u'kod': u'I9,I1,I1', u'sign': u'-,-', u'rhi': 0, u'eta': 1692, u'label': u'836a3b', u'fh': 0.07586616845714117, u'found': u'JI', u'N': 836, u'mtrx': u'matrix(3,[0,3,0,3,0,3,0,3,0])', u'ordj': u'9,1,1'}, {u'nh': 63.644586994565771, u'rlow': 1, u'tama': u'6,2,2', u'cond1': u'26*a-10', u'ainv2': u'[1,a,0,-23*a-24,69*a+33]', u'ainv1': u'[1,-a+1,0,23*a-47,-69*a+102]', u'cond2': u'-26*a+16', u'tor': 4, u'Lstar': 1.3043748959799999, u'ordD': u'6,2,2', u'kod': u'I6,I2,I2', u'sign': u'+,+', u'rhi': 1, u'eta': 1708, u'label': u'836b2a', u'fh': -0.28665957301952821, u'found': u'JI', u'N': 836, u'mtrx': u'matrix(4,[0,2,0,0,2,0,2,2,0,2,0,0,0,2,0,0])', u'ordj': u'6,2,2'}, {u'nh': 67.176983276444886, u'rlow': 1, u'tama': u'12,1,1', u'cond1': u'26*a-10', u'ainv2': u'[1,a,0,7*a+16,327*a+149]', u'ainv1': u'[1,-a+1,0,-7*a+23,-327*a+476]', u'cond2': u'-26*a+16', u'tor': 2, u'Lstar': 1.3043748959799999, u'ordD': u'12,1,1', u'kod': u'I12,I1,I1', u'sign': u'-,-', u'rhi': 1, u'eta': 1708, u'label': u'836b2c', u'fh': 0.059914017260444402, u'found': u'JI', u'N': 836, u'mtrx': u'matrix(4,[0,2,0,0,2,0,2,2,0,2,0,0,0,2,0,0])', u'ordj': u'12,1,1'}, {u'nh': 80.17912639899437, u'rlow': 1, u'tama': u'3,2,1', u'cond1': u'26*a-10', u'ainv2': u'[1,a,0,-373*a-384,5395*a+2621]', u'ainv1': u'[1,-a+1,0,373*a-757,-5395*a+8016]', u'cond2': u'-26*a+16', u'tor': 2, u'Lstar': 1.3043748959799999, u'ordD': u'3,4,1', u'kod': u'I3,I4,I1', u'sign': u'+,+', u'rhi': 1, u'eta': 1708, u'label': u'836b2b', u'fh': 0.05991401726044434, u'found': u'JI', u'N': 836, u'mtrx': u'matrix(4,[0,2,0,0,2,0,2,2,0,2,0,0,0,2,0,0])', u'ordj': u'3,4,1'}]
}}}

{{{id=26|
db.N1k.delete(ainv1='[a,a,a+1,19*a-24,-13*a+21]')
///
}}}

{{{id=25|
db.N1k.update({'Lstar':'REMOVE THIS CURVE'},ainv1='[a,a,a+1,19*a-24,-13*a+21]')
///
}}}

{{{id=18|
for x in range(len(test)):
    print type(test[x][3])
///
}}}

{{{id=17|
len(test)
///
0
}}}

{{{id=13|
k=0
for s in range(len(test)):
    if type(test[s][3]) != type(float(2)):
        print test[s][3]
///
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
}}}

{{{id=15|
def f_height(ainv):
    E=EllipticCurve(K,ainv)
    phi1=K.embeddings(RR)[0]
    A1=E.period_lattice(phi1).basis()
    B1=sqrt(matrix(2,2,(A1[0].real(),A1[0].imag(),A1[1].real(),A1[1].imag())).determinant())
    
    phi2=K.embeddings(RR)[1]
    A2=E.period_lattice(phi2).basis()
    B2=sqrt(matrix(2,2,(A2[0].real(),A2[0].imag(),A2[1].real(),A2[1].imag())).determinant())
    
    C=(-1/2)*log(B1*B2)
    return C
    
def n_height(E):
    A=EllipticCurve(K,E).short_weierstrass_model().a_invariants()
    B=log(max(4*(abs(A[3].norm())^3),27*((A[4].norm())^2)))
    return B
///
}}}

{{{id=29|
test=db('select ainv1 from N1k ORDER BY N,eta')
///
}}}

{{{id=30|
eval(test[0][0])
///
[1, a + 1, a, a, 0]
}}}

{{{id=31|
len(test)
///
721
}}}

{{{id=32|
def f_height(ainv):
    E=EllipticCurve(K,ainv)
    phi1=K.embeddings(RR)[0]
    A1=E.period_lattice(phi1).basis()
    B1=sqrt(matrix(2,2,(A1[0].real(),A1[0].imag(),A1[1].real(),A1[1].imag())).determinant())
    
    phi2=K.embeddings(RR)[1]
    A2=E.period_lattice(phi2).basis()
    B2=sqrt(matrix(2,2,(A2[0].real(),A2[0].imag(),A2[1].real(),A2[1].imag())).determinant())
    
    C=(-1/2)*log(B1*B2)
    return C
    
def n_height(E):
    A=EllipticCurve(K,E).short_weierstrass_model().a_invariants()
    B=log(max(4*(abs(A[3].norm())^3),27*((A[4].norm())^2)))
    return B
///
}}}

{{{id=14|
k=0
for t in range(len(test)):
    A=test[t]
    h=f_height(eval(A[0]))
    n=n_height(eval(A[0]))
    db.N1k.update({'fh':float(h), 'nh':float(n)}, ainv1=test[t][0])
    k+=1
    print k
///
WARNING: Output truncated!  
<html><a target='_new' href='/home/admin/7/cells/14/full_output.txt' class='file_link'>full_output.txt</a></html>



1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59

...

662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
}}}

{{{id=33|
f
///
}}}

{{{id=34|
temp=db('select N,eta,Lstar,fh,nh,ainv1 from N1k ORDER BY N,eta,Lstar,fh,nh')
///
}}}

{{{id=35|
for t in range(len(temp)):
    if type(temp[t][4]) != type(float(2)):
        print temp[t][3],temp[t][4], temp[5]
///
}}}

{{{id=16|
temp=db("select N,eta,Lstar,fh,nh,ainv1 from N1k ORDER BY N,eta,Lstar,fh,nh")
///
}}}

{{{id=36|
%time

N=0
lastchar1=ord('a')
L=1
lastchar2=ord('a')
test=[]
for s in range(len(temp)):
    A=temp[s]
    if temp[s][0] != temp[s-1][0]:            #this instance is a curve with a new norm than the previous entry
        N=int(temp[s][0])
        lastchar1=ord('a')
        L=1
        lastchar2=ord('a')
    else:
        if temp[s][1]==temp[s-1][1]:
            if temp[s][2]==temp[s-1][2]:
                lastchar2+=1
            else:
                L+=1
                lastchar2=ord('a')
        else:
            lastchar1+=1
            L=1
            lastchar2=ord('a')
    key=str(N)+chr(lastchar1)+str(L)+chr(lastchar2)
    db.N1k.update({'label': key},ainv1=A[5])
///
CPU time: 3.44 s,  Wall time: 20.62 s
}}}

{{{id=37|
temp2=db('select label,N,eta,Lstar,fh,nh,cond1,cond2,ainv1,ainv2,rlow,rhi,tor,sign,ordD,ordj,tama,kod from N1k ORDER BY N,eta,Lstar,fh,nh')
///
}}}

{{{id=39|
len(temp2)
///
721
}}}

{{{id=12|
def printer():
    J=open('/home/psharaba/ECD/Fulllist2.txt','w')
    for y in temp2:
        S=[]
        for entry in y:
            s=str(entry)
            s.replace(' ','')
            S.append(s)
        J.write(' '.join(S)+'\n')
///
}}}

{{{id=38|
printer()
///
}}}

{{{id=40|

///
}}}