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SageMath
sage: E = EllipticCurve("9680.bb1")
sage: E.isogeny_class()
Elliptic curves in class 9680.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 9680.bb1 | 9680bc4 | [0, -1, 0, -859140, -306223300] | [2] | 103680 | |
| 9680.bb2 | 9680bc3 | [0, -1, 0, -53885, -4735828] | [2] | 51840 | |
| 9680.bb3 | 9680bc2 | [0, -1, 0, -12140, -286900] | [2] | 34560 | |
| 9680.bb4 | 9680bc1 | [0, -1, 0, -5485, 154992] | [2] | 17280 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9680.bb have rank \(0\).
Modular form 9680.2.a.bb
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.
