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SageMath
sage: E = EllipticCurve("gx1")
sage: E.isogeny_class()
Elliptic curves in class 110400.gx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 110400.gx1 | 110400dq4 | [0, 1, 0, -176640033, 903552768063] | [2] | 7077888 | |
| 110400.gx2 | 110400dq6 | [0, 1, 0, -41328033, -87610415937] | [2] | 14155776 | |
| 110400.gx3 | 110400dq3 | [0, 1, 0, -11328033, 13339584063] | [2, 2] | 7077888 | |
| 110400.gx4 | 110400dq2 | [0, 1, 0, -11040033, 14115168063] | [2, 2] | 3538944 | |
| 110400.gx5 | 110400dq1 | [0, 1, 0, -672033, 232416063] | [2] | 1769472 | \(\Gamma_0(N)\)-optimal |
| 110400.gx6 | 110400dq5 | [0, 1, 0, 14063967, 64656816063] | [2] | 14155776 |
Rank
sage: E.rank()
The elliptic curves in class 110400.gx have rank \(1\).
Complex multiplication
The elliptic curves in class 110400.gx do not have complex multiplication.Modular form 110400.2.a.gx
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
