# Oscar code for working with elliptic curve 6.6.453789.1-43.1-a2
# If you have not already loaded the Oscar package, you should type "using Oscar;" before running the code below.
# (Note that not all these functions may be available, and some may take a long time to execute.)


# Define the base number field: 
Qx, x = polynomial_ring(QQ); K, a = number_field(Qx([1, -8, 8, 6, -6, -1, 1]))

# Define the curve: 
E = elliptic_curve([K([-2,1,1,0,0,0]),K([1,-1,-3,0,1,0]),K([-2,6,-2,-5,1,1]),K([-2,8,1,-3,0,0]),K([0,-5,2,5,-1,-1])])

# Compute the conductor: 
conductor(E)

# Compute the norm of the conductor: 
norm(conductor(E))

# Compute the discriminant: 
discriminant(E)

# Compute the norm of the discriminant: 
norm(discriminant(E))

# Compute the j-invariant: 
j_invariant(E)