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SageMath
sage: E = EllipticCurve("2880.m1")
sage: E.isogeny_class()
Elliptic curves in class 2880.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 2880.m1 | 2880i3 | [0, 0, 0, -1488, 22088] | [2] | 1152 | |
| 2880.m2 | 2880i4 | [0, 0, 0, -1308, 27632] | [2] | 2304 | |
| 2880.m3 | 2880i1 | [0, 0, 0, -48, -88] | [2] | 384 | \(\Gamma_0(N)\)-optimal |
| 2880.m4 | 2880i2 | [0, 0, 0, 132, -592] | [2] | 768 |
Rank
sage: E.rank()
The elliptic curves in class 2880.m have rank \(0\).
Modular form 2880.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
