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SageMath
sage: E = EllipticCurve("m1")
sage: E.isogeny_class()
Elliptic curves in class 2880.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.m1 | 2880i3 | \([0, 0, 0, -1488, 22088]\) | \(488095744/125\) | \(93312000\) | \([2]\) | \(1152\) | \(0.51524\) | |
| 2880.m2 | 2880i4 | \([0, 0, 0, -1308, 27632]\) | \(-20720464/15625\) | \(-186624000000\) | \([2]\) | \(2304\) | \(0.86181\) | |
| 2880.m3 | 2880i1 | \([0, 0, 0, -48, -88]\) | \(16384/5\) | \(3732480\) | \([2]\) | \(384\) | \(-0.034070\) | \(\Gamma_0(N)\)-optimal |
| 2880.m4 | 2880i2 | \([0, 0, 0, 132, -592]\) | \(21296/25\) | \(-298598400\) | \([2]\) | \(768\) | \(0.31250\) |
Rank
sage: E.rank()
The elliptic curves in class 2880.m have rank \(0\).
Complex multiplication
The elliptic curves in class 2880.m do not have complex multiplication.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.
