Show commands for:
SageMath
sage: E = EllipticCurve("9408.bw1")
sage: E.isogeny_class()
Elliptic curves in class 9408.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 9408.bw1 | 9408db4 | [0, 1, 0, -4214849, 3329185215] | [2] | 147456 | |
| 9408.bw2 | 9408db5 | [0, 1, 0, -2866369, -1850890945] | [2] | 294912 | |
| 9408.bw3 | 9408db3 | [0, 1, 0, -326209, 25271231] | [2, 2] | 147456 | |
| 9408.bw4 | 9408db2 | [0, 1, 0, -263489, 51927231] | [2, 2] | 73728 | |
| 9408.bw5 | 9408db1 | [0, 1, 0, -12609, 1199295] | [2] | 36864 | \(\Gamma_0(N)\)-optimal |
| 9408.bw6 | 9408db6 | [0, 1, 0, 1210431, 196452927] | [2] | 294912 |
Rank
sage: E.rank()
The elliptic curves in class 9408.bw have rank \(0\).
Modular form 9408.2.a.bw
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
