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SageMath
sage: E = EllipticCurve("22743.f1")
sage: E.isogeny_class()
Elliptic curves in class 22743.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 22743.f1 | 22743n6 | [1, -1, 1, -2547284, -1564182084] | [2] | 221184 | |
| 22743.f2 | 22743n4 | [1, -1, 1, -159269, -24390012] | [2, 2] | 110592 | |
| 22743.f3 | 22743n3 | [1, -1, 1, -126779, 17301156] | [2] | 110592 | |
| 22743.f4 | 22743n5 | [1, -1, 1, -110534, -39634320] | [2] | 221184 | |
| 22743.f5 | 22743n2 | [1, -1, 1, -13064, -119982] | [2, 2] | 55296 | |
| 22743.f6 | 22743n1 | [1, -1, 1, 3181, -16014] | [2] | 27648 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22743.f have rank \(1\).
Modular form 22743.2.a.f
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
