# Oscar code for working with elliptic curve 4.4.2304.1-576.1-b5
# 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, 0, -4, 0, 1]))

# Define the curve: 
E = elliptic_curve([K([0,-3,0,1]),K([-1,0,0,0]),K([0,-3,0,1]),K([-73,-150,0,50]),K([6,12,0,-4])])

# 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)