# Oscar code for working with elliptic curve 6.6.1528713.1-64.1-g1
# 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, -3, 3, 7, -3, -3, 1]))

# Define the curve: 
E = elliptic_curve([K([1,0,0,0,0,0]),K([-5,-6,11,3,-5,1]),K([-1,2,7,-3,-3,1]),K([-118,0,0,0,0,0]),K([-316,236,-438,-117,199,-40])])

# 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)