# Oscar code for working with elliptic curve 4.4.19025.1-20.2-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([44, 14, -13, -2, 1]))

# Define the curve: 
E = elliptic_curve([K([-3,1/2,1/2,0]),K([-5,1/2,1/2,0]),K([1,-3,-1/2,1/2]),K([-1621,430,240,-66]),K([-21072,5515,6233/2,-1695/2])])

# 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)