# SageMath code for working with elliptic curve isogeny class 75.c


# Define the isogeny class: 
E = EllipticCurve([0, -1, 1, -8, -7])
E.isogeny_class()

# Mordell-Weil rank: 
E.rank()

# q-expansion of modular form: 
E.q_eigenform(20)

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

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

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