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SageMath
sage: E = EllipticCurve("5040.d1")
sage: E.isogeny_class()
Elliptic curves in class 5040.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 5040.d1 | 5040bd3 | [0, 0, 0, -16203, -793798] | [2] | 8192 | |
| 5040.d2 | 5040bd2 | [0, 0, 0, -1083, -10582] | [2, 2] | 4096 | |
| 5040.d3 | 5040bd1 | [0, 0, 0, -363, 2522] | [2] | 2048 | \(\Gamma_0(N)\)-optimal |
| 5040.d4 | 5040bd4 | [0, 0, 0, 2517, -66022] | [2] | 8192 |
Rank
sage: E.rank()
The elliptic curves in class 5040.d have rank \(1\).
Modular form 5040.2.a.d
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.
