Error when computing torsion group
 
  
 
 
     
 
 
 
 
 
 
 
    
        
        asked 0 years ago  
 
 Hasan gravatar image  
 
 
 
 
    
        
        updated 0 years ago  
 
 
 
 
 
I am trying to run this code
 
t = var('t')
K.<a> = NumberField(20*t^4 + 40*t^3 + 28*t^2 + 8*t + 1) 
EK = EllipticCurve(K,[0,-3/2,0,1/2,0]) 
print(EK.torsion_subgroup())
 
However, Sage is throwing the following error:
 
y^2 = x^3 + 12*x^2 defines a singular curve
 
I am not exactly sure what the problem is since the original curve is a nonsingular curve. On the other hand, it appears that when I use K to be the full 5-division field, for example, there is no error. However, that field is much larger than what I want to consider. 
 
Any ideas what's going wrong?
 
Thanks.
 
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Comments
The error occurs at this linewhile computing bound. It looks like a bug that should be reported at https://github.com/sagemath/sage/issues
Max Alekseyev gravatar imageMax Alekseyev (
    
        0 years ago
    )
@Max Alekseyev, Thanks, I will report it.
Hasan gravatar imageHasan (
    
        0 years ago
    )
Just for the record, https://github.com/sagemath/sage/issu...
Max Alekseyev gravatar imageMax Alekseyev (
    
        0 years ago
    )
My sage version works:
sage: t = var('t');
....: K.<a> = NumberField(20*t^4 + 40*t^3 + 28*t^2 + 8*t + 1)
....: EK = EllipticCurve(K, [0, -3/2, 0, 1/2, 0])
sage: EK.torsion_subgroup()
Torsion Subgroup isomorphic to Z/2 + Z/2 associated to the Elliptic Curve defined by y^2 = x^3 + (-3/2)*x^2 + 1/2*x over Number Field in a with defining polynomial 20*t^4 + 40*t^3 + 28*t^2 + 8*t + 1
sage: print(EK.torsion_points())
[(0 : 1 : 0), (1/2 : 0 : 1), (1 : 0 : 1), (0 : 0 : 1)]
sage: version()
'SageMath version 10.5, Release Date: 2024-12-04'
dan_fulea gravatar imagedan_fulea (
    
        0 years ago
    )
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