# Oscar code for working with elliptic curve 6.6.434581.1-71.1-b1
# 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([-1, -2, 4, 5, -4, -2, 1]))

# Define the curve: 
E = elliptic_curve([K([-2,4,12,-10,-6,3]),K([-3,-5,4,6,0,-1]),K([-1,0,4,-3,-2,1]),K([366,208,-1840,604,798,-297]),K([4476,3003,-22010,6587,9442,-3433])])

# 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)