Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 612.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
612.d1 | 612a1 | -optimal | ||||||
612.d2 | 612a2 |
Rank
sage: E.rank()
The elliptic curves in class 612.d have rank .
Complex multiplication
The elliptic curves in class 612.d do not have complex multiplication.Modular form 612.2.a.d
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.