# Oscar code for working with elliptic curve 6.6.300125.1-64.1-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, 7, 2, -7, -1, 1]))

# Define the curve: 
E = elliptic_curve([K([-2,-10,4,14,1,-2]),K([10,32,-22,-50,-2,7]),K([-5,-18,13,29,1,-4]),K([16,51,-34,-79,-3,11]),K([8,47,-37,-55,1,7])])

# 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)