Show commands:
SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 9408.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.co1 | 9408bb4 | \([0, 1, 0, -358353, 82449135]\) | \(2640279346000/3087\) | \(5950381473792\) | \([2]\) | \(55296\) | \(1.7343\) | |
| 9408.co2 | 9408bb3 | \([0, 1, 0, -22213, 1304939]\) | \(-10061824000/352947\) | \(-42520434281472\) | \([2]\) | \(27648\) | \(1.3878\) | |
| 9408.co3 | 9408bb2 | \([0, 1, 0, -5553, 49167]\) | \(9826000/5103\) | \(9836344885248\) | \([2]\) | \(18432\) | \(1.1850\) | |
| 9408.co4 | 9408bb1 | \([0, 1, 0, 1307, 6635]\) | \(2048000/1323\) | \(-159385218048\) | \([2]\) | \(9216\) | \(0.83846\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9408.co have rank \(1\).
Complex multiplication
The elliptic curves in class 9408.co do not have complex multiplication.Modular form 9408.2.a.co
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
