# Oscar code for working with elliptic curve 2.0.11.1-46656.5-d1
# 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([3, -1, 1]))

# Define the curve: 
E = elliptic_curve([K([0,0]),K([0,0]),K([0,0]),K([15,-6]),K([-19,-14])])

# 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)