Show commands for:
SageMath
sage: E = EllipticCurve("11760.br1")
sage: E.isogeny_class()
Elliptic curves in class 11760.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 11760.br1 | 11760ce3 | [0, 1, 0, -88216, -10113580] | [2] | 49152 | |
| 11760.br2 | 11760ce2 | [0, 1, 0, -5896, -136396] | [2, 2] | 24576 | |
| 11760.br3 | 11760ce1 | [0, 1, 0, -1976, 31380] | [2] | 12288 | \(\Gamma_0(N)\)-optimal |
| 11760.br4 | 11760ce4 | [0, 1, 0, 13704, -834156] | [2] | 49152 |
Rank
sage: E.rank()
The elliptic curves in class 11760.br have rank \(0\).
Modular form 11760.2.a.br
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
