Cremona_table_conductor95-116

338 days ago by Paul_Sharaba

x=var('x') K.<a>=NumberField(x^2-x-1) emb=K.embeddings(RR) 
       
def db(mtrx): E=EllipticCurve(K,mtrx) N=E.conductor() print 'conductor', N print 'a_1 , a_2, a_3, a_4, a_6', E.a_invariants() print 'rank', 0 T=E.torsion_order() print '|T|', T disc = E.discriminant() disc_signs = [e(disc).sign() for e in emb] print 's_signs', disc_signs F=[c for c, _ in E.conductor().factor()] Delta=[E.discriminant().valuation(c) for c in F] print 'Delta',Delta J=K(E.j_invariant().denominator_ideal().gens_reduced()[0]).factor() for j in J: l=[];i=0 l.append(J[i][1]) i+=1 print 'ord(j-inv.)', l Tm=E.tamagawa_numbers() print 'Tamagawa Numbers', Tm e=K.primes_above(N) n=0 for i in e: print 'kodaira', E.kodaira_symbol(e[n]) n+=1 
       
 
        
Traceback (click to the left of this block for traceback)
...
SyntaxError: invalid syntax
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_65.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("QT1bYSsxLGEtMSwxLC1hKzEsLTFdCkI9W2ErMSwwLDAsMSwwXQpDPVthLC1hKzEsMCwxLDBdCkQ9WzEsMCwxLC0xLC0yXQpFPVthLGEtMSxhKzEsLWEsLWFdXQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmprmygEm/___code___.py", line 7
    E=[a,a-_sage_const_1 ,a+_sage_const_1 ,-a,-a]]
                                                 ^
SyntaxError: invalid syntax
db([a+1,a-1,1,-a+1,-1]) 
        
conductor Fractional ideal (-2*a - 9)
a_1 , a_2, a_3, a_4, a_6 (a + 1, a - 1, 1, -a + 1, -1)
rank 0
|T| 6
s_signs [-1, 1]
Delta [1, 3]
ord(j-inv.) [1]
ord(j-inv.) [1]
Tamagawa Numbers [1, 3]
kodaira I3
kodaira I1
conductor Fractional ideal (-2*a - 9)
a_1 , a_2, a_3, a_4, a_6 (a + 1, a - 1, 1, -a + 1, -1)
rank 0
|T| 6
s_signs [-1, 1]
Delta [1, 3]
ord(j-inv.) [1]
ord(j-inv.) [1]
Tamagawa Numbers [1, 3]
kodaira I3
kodaira I1
db([a+1,0,0,1,0]) 
        
conductor Fractional ideal (9*a - 3)
a_1 , a_2, a_3, a_4, a_6 (a + 1, 0, 0, 1, 0)
rank 0
|T| 4
s_signs [-1, -1]
Delta [2, 1]
ord(j-inv.) [2]
ord(j-inv.) [2]
Tamagawa Numbers [2, 1]
kodaira I2
kodaira I1
conductor Fractional ideal (9*a - 3)
a_1 , a_2, a_3, a_4, a_6 (a + 1, 0, 0, 1, 0)
rank 0
|T| 4
s_signs [-1, -1]
Delta [2, 1]
ord(j-inv.) [2]
ord(j-inv.) [2]
Tamagawa Numbers [2, 1]
kodaira I2
kodaira I1
db([a,-a+1,0,1,0]) 
        
conductor Fractional ideal (9*a - 6)
a_1 , a_2, a_3, a_4, a_6 (a, -a + 1, 0, 1, 0)
rank 0
|T| 4
s_signs [-1, -1]
Delta [2, 1]
ord(j-inv.) [2]
ord(j-inv.) [2]
Tamagawa Numbers [2, 1]
kodaira I2
kodaira I1
conductor Fractional ideal (9*a - 6)
a_1 , a_2, a_3, a_4, a_6 (a, -a + 1, 0, 1, 0)
rank 0
|T| 4
s_signs [-1, -1]
Delta [2, 1]
ord(j-inv.) [2]
ord(j-inv.) [2]
Tamagawa Numbers [2, 1]
kodaira I2
kodaira I1
db([1,0,1,-1,-2]) 
        
conductor Fractional ideal (10)
a_1 , a_2, a_3, a_4, a_6 (1, 0, 1, -1, -2)
rank 0
|T| 3
s_signs [-1, -1]
Delta [1, 8]
ord(j-inv.) [1]
Tamagawa Numbers [1, 3]
kodaira IV*
kodaira I1
conductor Fractional ideal (10)
a_1 , a_2, a_3, a_4, a_6 (1, 0, 1, -1, -2)
rank 0
|T| 3
s_signs [-1, -1]
Delta [1, 8]
ord(j-inv.) [1]
Tamagawa Numbers [1, 3]
kodaira IV*
kodaira I1
db([a,a-1,a+1,-a,-a]) 
        
conductor Fractional ideal (10)
a_1 , a_2, a_3, a_4, a_6 (a, a - 1, a + 1, -a, -a)
rank 0
|T| 5
s_signs [-1, -1]
Delta [1, 2]
ord(j-inv.) [1]
Tamagawa Numbers [1, 1]
kodaira II
kodaira I1
conductor Fractional ideal (10)
a_1 , a_2, a_3, a_4, a_6 (a, a - 1, a + 1, -a, -a)
rank 0
|T| 5
s_signs [-1, -1]
Delta [1, 2]
ord(j-inv.) [1]
Tamagawa Numbers [1, 1]
kodaira II
kodaira I1
db([1,-1,a,-a,0]) 
        
conductor Fractional ideal (2*a + 10)
a_1 , a_2, a_3, a_4, a_6 (1, -1, a, -a, 0)
rank 0
|T| 5
s_signs [-1, -1]
Delta [1, 1]
ord(j-inv.) [1]
ord(j-inv.) [1]
Tamagawa Numbers [1, 1]
kodaira I1
kodaira I1
conductor Fractional ideal (2*a + 10)
a_1 , a_2, a_3, a_4, a_6 (1, -1, a, -a, 0)
rank 0
|T| 5
s_signs [-1, -1]
Delta [1, 1]
ord(j-inv.) [1]
ord(j-inv.) [1]
Tamagawa Numbers [1, 1]
kodaira I1
kodaira I1