Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 462f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
462.g4 | 462f1 | -optimal | ||||||
462.g3 | 462f2 | |||||||
462.g2 | 462f3 | |||||||
462.g1 | 462f4 |
Rank
sage: E.rank()
The elliptic curves in class 462f have rank .
Complex multiplication
The elliptic curves in class 462f do not have complex multiplication.Modular form 462.2.a.f
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.