# SageMath code for working with elliptic curve isogeny class 6.6.371293.1-79.4-c
# (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([-1, -3, 6, 4, -5, -1, 1]))

# Define the isogeny class: 
E = EllipticCurve([K([3,2,-4,-4,1,1]),K([2,-2,-4,1,1,0]),K([-2,1,1,0,0,0]),K([11,9,-44,16,13,-6]),K([-14,-30,107,-38,-33,15])])
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