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SageMath
sage: E = EllipticCurve("d1")
sage: E.isogeny_class()
Elliptic curves in class 720.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 720.d1 | 720c5 | [0, 0, 0, -28803, -1881502] | [2] | 1024 | |
| 720.d2 | 720c3 | [0, 0, 0, -1803, -29302] | [2, 2] | 512 | |
| 720.d3 | 720c6 | [0, 0, 0, -723, -64078] | [2] | 1024 | |
| 720.d4 | 720c2 | [0, 0, 0, -183, 182] | [2, 2] | 256 | |
| 720.d5 | 720c1 | [0, 0, 0, -138, 623] | [2] | 128 | \(\Gamma_0(N)\)-optimal |
| 720.d6 | 720c4 | [0, 0, 0, 717, 1442] | [2] | 512 |
Rank
sage: E.rank()
The elliptic curves in class 720.d have rank \(0\).
Complex multiplication
The elliptic curves in class 720.d do not have complex multiplication.Modular form 720.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
