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SageMath
sage: E = EllipticCurve("bg1")
sage: E.isogeny_class()
Elliptic curves in class 18480.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 18480.bg1 | 18480cd5 | [0, -1, 0, -48787200, 131177938752] | [4] | 491520 | |
| 18480.bg2 | 18480cd4 | [0, -1, 0, -3049200, 2050417152] | [2, 4] | 245760 | |
| 18480.bg3 | 18480cd6 | [0, -1, 0, -3034080, 2071742400] | [4] | 491520 | |
| 18480.bg4 | 18480cd3 | [0, -1, 0, -407120, -52590720] | [2] | 245760 | |
| 18480.bg5 | 18480cd2 | [0, -1, 0, -191520, 31752000] | [2, 2] | 122880 | |
| 18480.bg6 | 18480cd1 | [0, -1, 0, 560, 1480192] | [2] | 61440 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18480.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 18480.bg do not have complex multiplication.Modular form 18480.2.a.bg
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
