Show commands for:
SageMath
sage: E = EllipticCurve("47040.gg1")
sage: E.isogeny_class()
Elliptic curves in class 47040.gg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 47040.gg1 | 47040df4 | [0, 1, 0, -352865, 80555775] | [2] | 393216 | |
| 47040.gg2 | 47040df2 | [0, 1, 0, -23585, 1067583] | [2, 2] | 196608 | |
| 47040.gg3 | 47040df1 | [0, 1, 0, -7905, -258945] | [2] | 98304 | \(\Gamma_0(N)\)-optimal |
| 47040.gg4 | 47040df3 | [0, 1, 0, 54815, 6728063] | [2] | 393216 |
Rank
sage: E.rank()
The elliptic curves in class 47040.gg have rank \(0\).
Modular form 47040.2.a.gg
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.
