3Selmer

586 days ago by jen

R.<y> = QQ['y'] E = EllipticCurve('37a') E.heegner_discriminants(30) D=-7; #K.<a>=QuadraticField(D); K=QQ; EK=E.change_ring(K); P=E.heegner_point(D) [ell for ell in prime_range(50) if P.satisfies_kolyvagin_hypothesis(ell)] ell=11 ell=11 f = EK.division_polynomial(3) g,d = sage.schemes.elliptic_curves.heegner.make_monic(f) Lx.<b_x> = NumberField(g) ELx = EK.change_ring(Lx) R.<y>=Lx['y'] fy = E.defining_polynomial()(b_x/d,y,1); print fy.parent() ypoly=factor(fy)[0][0]; ypoly1, dd= sage.schemes.elliptic_curves.heegner.make_monic(ypoly) L.<b> = Lx.extension(ypoly1) EL = E.change_ring(L); print L print 3*EL.lift_x(b_x/d) I3 = [x[0] for x in L.factor(3)] Iell = [x[0] for x in L.factor(ell)] time G=L.selmer_group(I3+Iell,3) 
        
Univariate Polynomial Ring in y over Number Field in b_x with defining
polynomial x^4 - 18*x^2 + 27*x - 27
Number Field in b with defining polynomial y^2 + 27*y - 27*b_x^3 +
243*b_x over its base field
(0 : 1 : 0)
Time: CPU 1.11 s, Wall: 1.61 s
Univariate Polynomial Ring in y over Number Field in b_x with defining polynomial x^4 - 18*x^2 + 27*x - 27
Number Field in b with defining polynomial y^2 + 27*y - 27*b_x^3 + 243*b_x over its base field
(0 : 1 : 0)
Time: CPU 1.11 s, Wall: 1.61 s
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
L.selmer_group(I3+Iell, 3) 
        
Traceback (click to the left of this block for traceback)
...
NameError: name 'L' is not defined
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_13.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("TC5zZWxtZXJfZ3JvdXAoSTMrSWVsbCwgMyk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpaks1FJ/___code___.py", line 3, in <module>
    exec compile(u'L.selmer_group(I3+Iell, _sage_const_3 )
  File "", line 1, in <module>
    
NameError: name 'L' is not defined
 
       
lis=range(5)+range(2); lis 
        
[0, 1, 2, 3, 4, 0, 1]
[0, 1, 2, 3, 4, 0, 1]
1+9 
        
10
10