# Oscar code for working with elliptic curve 4.4.1600.1-16.1-a12
# 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([4, 0, -6, 0, 1]))

# Define the curve: 
E = elliptic_curve([K([0,0,0,0]),K([0,3,0,-1/2]),K([0,0,0,0]),K([-18,22,3,-4]),K([55,-64,-10,12])])

# 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)