Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1728.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1728.c1 | 1728e3 | |||||||
1728.c2 | 1728e1 | -optimal | ||||||
1728.c3 | 1728e2 |
Rank
sage: E.rank()
The elliptic curves in class 1728.c have rank .
Complex multiplication
The elliptic curves in class 1728.c do not have complex multiplication.Modular form 1728.2.a.c
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 LMFDB numbering.
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.