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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 2880.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.x1 | 2880s5 | \([0, 0, 0, -115212, 15052016]\) | \(1770025017602/75\) | \(7166361600\) | \([4]\) | \(8192\) | \(1.3759\) | |
| 2880.x2 | 2880s3 | \([0, 0, 0, -7212, 234416]\) | \(868327204/5625\) | \(268738560000\) | \([2, 2]\) | \(4096\) | \(1.0293\) | |
| 2880.x3 | 2880s6 | \([0, 0, 0, -2892, 512624]\) | \(-27995042/1171875\) | \(-111974400000000\) | \([2]\) | \(8192\) | \(1.3759\) | |
| 2880.x4 | 2880s2 | \([0, 0, 0, -732, -1456]\) | \(3631696/2025\) | \(24186470400\) | \([2, 2]\) | \(2048\) | \(0.68273\) | |
| 2880.x5 | 2880s1 | \([0, 0, 0, -552, -4984]\) | \(24918016/45\) | \(33592320\) | \([2]\) | \(1024\) | \(0.33616\) | \(\Gamma_0(N)\)-optimal |
| 2880.x6 | 2880s4 | \([0, 0, 0, 2868, -11536]\) | \(54607676/32805\) | \(-1567283281920\) | \([2]\) | \(4096\) | \(1.0293\) |
Rank
sage: E.rank()
The elliptic curves in class 2880.x have rank \(1\).
Complex multiplication
The elliptic curves in class 2880.x do not have complex multiplication.Modular form 2880.2.a.x
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.
