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I am trying to run this code

t = var('t')

K. = NumberField(20t^4 + 40t^3 + 28t^2 + 8t + 1)

EK = EllipticCurve(K,[0,3/2,0,1/2,0])

print(EK.torsion_subgroup())

I am trying to run this code

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]) EllipticCurve(K,[0,-3/2,0,1/2,0]) 
print(EK.torsion_subgroup())

However, Sage is throwing the following error:

y^2 = x^3 + 25*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.

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 + 25*x^2 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.