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SageMath
sage: E = EllipticCurve("er1")
sage: E.isogeny_class()
Elliptic curves in class 73920.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 73920.er1 | 73920gd6 | [0, 1, 0, -195148801, 1049228361215] | [2] | 3932160 | |
| 73920.er2 | 73920gd4 | [0, 1, 0, -12196801, 16391140415] | [2, 2] | 1966080 | |
| 73920.er3 | 73920gd5 | [0, 1, 0, -12136321, 16561802879] | [2] | 3932160 | |
| 73920.er4 | 73920gd3 | [0, 1, 0, -1628481, -422354241] | [2] | 1966080 | |
| 73920.er5 | 73920gd2 | [0, 1, 0, -766081, 253249919] | [2, 2] | 983040 | |
| 73920.er6 | 73920gd1 | [0, 1, 0, 2239, 11843775] | [2] | 491520 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.er have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.er do not have complex multiplication.Modular form 73920.2.a.er
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
