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SageMath
sage: E = EllipticCurve("16562.bv1")
sage: E.isogeny_class()
Elliptic curves in class 16562bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 16562.bv5 | 16562bo1 | [1, 1, 1, -4313, -222461] | [2] | 34560 | \(\Gamma_0(N)\)-optimal |
| 16562.bv4 | 16562bo2 | [1, 1, 1, -87123, -9927793] | [2] | 69120 | |
| 16562.bv6 | 16562bo3 | [1, 1, 1, 37092, 4630205] | [2] | 103680 | |
| 16562.bv3 | 16562bo4 | [1, 1, 1, -294148, 50208829] | [2] | 207360 | |
| 16562.bv2 | 16562bo5 | [1, 1, 1, -1412083, 647136433] | [2] | 311040 | |
| 16562.bv1 | 16562bo6 | [1, 1, 1, -22611443, 41375346865] | [2] | 622080 |
Rank
sage: E.rank()
The elliptic curves in class 16562bo have rank \(1\).
Modular form 16562.2.a.bv
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
