# Oscar code for working with elliptic curve 4.4.19025.1-20.1-a2
# 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([-4,-7/2,0,1/2]),K([5,-7/2,-1,1/2]),K([-3,-9/2,0,1/2]),K([208,-390,-327/2,145/2]),K([2658,-10503/2,-2209,1941/2])])

# 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)