# Oscar code for working with elliptic curve 4.4.18496.1-4.1-a1
# 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([2, 12, -11, -2, 1]))

# Define the curve: 
E = elliptic_curve([K([-22/9,-14/9,1/3,1/9]),K([32/9,-5/9,-2/3,1/9]),K([-32/9,14/9,2/3,-1/9]),K([38/9,34/9,-2/3,-5/9]),K([11/9,34/9,-2/3,-5/9])])

# 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)