Show commands:
SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 389844.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 389844.cv1 | 389844cv2 | \([0, 0, 0, -1081479, 432883150]\) | \(6371214852688/77571\) | \(1703158725655296\) | \([2]\) | \(3981312\) | \(2.0710\) | |
| 389844.cv2 | 389844cv1 | \([0, 0, 0, -69384, 6386317]\) | \(26919436288/2738853\) | \(3758412764787408\) | \([2]\) | \(1990656\) | \(1.7244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 389844.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 389844.cv do not have complex multiplication.Modular form 389844.2.a.cv
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
