conjectural_order_of_sha

330 days ago by arabindr

ch = var('ch') K.<a> = NumberField(ch^2 - ch - 1) E=EllipticCurve(K, [1,a+1,a,a,0]).global_minimal_model() 
       
def real_periods(E): embs = K.embeddings(RR) v=[1,1] i = 0 while i < 2: t = E.period_lattice(embs[i]).basis() if real(t[1])==0: v[i] = 2*t[0] else: v[i] = t[0] i+=1 return v[0]*v[1] 
       
real_periods(F) 
        
Traceback (click to the left of this block for traceback)
...
NameError: name 'F' is not defined
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_4.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cmVhbF9wZXJpb2RzKEYp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmp4pfbt1/___code___.py", line 2, in <module>
    exec compile(u'real_periods(F)
  File "", line 1, in <module>
    
NameError: name 'F' is not defined
def conjectural_sha(E, reg=1, Lstar=1): M = E.tamagawa_product_bsd() print M sha = RR(sqrt(5))*Lstar*(E.torsion_order())^2/((real_periods(E))*reg*M) return sha 
       
conjectural_sha(E,1,0.359928959498039) 
        
1
0.999999999999999
1
0.999999999999999
F = EllipticCurve(K, [0,-a-1,1,a,0]) 
       
conjectural_sha(F,0.0771542842715149,0.657814883009960) 
        
1
4.00000000000002
1
4.00000000000002
F.torsion_order() 
        
3
3
RR(sqrt(5))*0.657*(3)^2/(3.534*6.067*0.15430*1) 
        
3.99656071419878
3.99656071419878