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SageMath
sage: E = EllipticCurve("dz1")
sage: E.isogeny_class()
Elliptic curves in class 33600.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 33600.dz1 | 33600gi4 | [0, 1, 0, -2150433, -1214488737] | [2] | 393216 | |
| 33600.dz2 | 33600gi6 | [0, 1, 0, -1462433, 673687263] | [2] | 786432 | |
| 33600.dz3 | 33600gi3 | [0, 1, 0, -166433, -9304737] | [2, 2] | 393216 | |
| 33600.dz4 | 33600gi2 | [0, 1, 0, -134433, -19000737] | [2, 2] | 196608 | |
| 33600.dz5 | 33600gi1 | [0, 1, 0, -6433, -440737] | [2] | 98304 | \(\Gamma_0(N)\)-optimal |
| 33600.dz6 | 33600gi5 | [0, 1, 0, 617567, -71240737] | [2] | 786432 |
Rank
sage: E.rank()
The elliptic curves in class 33600.dz have rank \(1\).
Complex multiplication
The elliptic curves in class 33600.dz do not have complex multiplication.Modular form 33600.2.a.dz
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.
