# Oscar code for working with elliptic curve 4.4.12725.1-16.1-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([29, 11, -10, -2, 1]))

# Define the curve: 
E = elliptic_curve([K([1,1,0,0]),K([0,5,1,-1]),K([-6,-1,1,0]),K([-4719,1094,984,-273]),K([94946,-21474,-19757,5413])])

# 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)