Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 133570k
sage: E.isogeny_class().curves
Rank
sage: E.rank()
The elliptic curves in class 133570k have rank .
Complex multiplication
The elliptic curves in class 133570k do not have complex multiplication.Modular form 133570.2.a.k
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The entry is the smallest degree of a cyclic isogeny between the -th and -th curve in the isogeny class, in the Cremona numbering.
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.