# SageMath code for working with elliptic curve isogeny class 2.2.56.1-56.1-b
# (Note that not all these functions may be available, and some may take a long time to execute.)


# Define the base number field: 
R.<x> = PolynomialRing(QQ);  K.<a> = NumberField(R([-14, 0, 1]))

# Define the isogeny class: 
E = EllipticCurve([K([0,1]),K([1,0]),K([0,1]),K([-33003,-8820]),K([3414635,912600])])
E.isogeny_class()

# Compute the Mordell-Weil rank: 
E.rank()

# Isogeny matrix: 
E.isogeny_class().matrix()

# Isogeny graph: 
E.isogeny_class().graph().plot(edge_labels=True)

# List of curves in the isogeny class: 
E.isogeny_class().curves