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SageMath
sage: E = EllipticCurve("58800.bx1")
sage: E.isogeny_class()
Elliptic curves in class 58800.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 58800.bx1 | 58800fj4 | [0, -1, 0, -2205408, -1259786688] | [2] | 1179648 | |
| 58800.bx2 | 58800fj2 | [0, -1, 0, -147408, -16754688] | [2, 2] | 589824 | |
| 58800.bx3 | 58800fj1 | [0, -1, 0, -49408, 4021312] | [2] | 294912 | \(\Gamma_0(N)\)-optimal |
| 58800.bx4 | 58800fj3 | [0, -1, 0, 342592, -104954688] | [2] | 1179648 |
Rank
sage: E.rank()
The elliptic curves in class 58800.bx have rank \(1\).
Modular form 58800.2.a.bx
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.
