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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 11616.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11616.k1 | 11616e3 | \([0, -1, 0, -3912, 95460]\) | \(7301384/3\) | \(2721117696\) | \([2]\) | \(10240\) | \(0.77273\) | |
| 11616.k2 | 11616e2 | \([0, -1, 0, -2097, -35583]\) | \(140608/3\) | \(21768941568\) | \([2]\) | \(10240\) | \(0.77273\) | |
| 11616.k3 | 11616e1 | \([0, -1, 0, -282, 1080]\) | \(21952/9\) | \(1020419136\) | \([2, 2]\) | \(5120\) | \(0.42615\) | \(\Gamma_0(N)\)-optimal |
| 11616.k4 | 11616e4 | \([0, -1, 0, 928, 6888]\) | \(97336/81\) | \(-73470177792\) | \([2]\) | \(10240\) | \(0.77273\) |
Rank
sage: E.rank()
The elliptic curves in class 11616.k have rank \(0\).
Complex multiplication
The elliptic curves in class 11616.k do not have complex multiplication.Modular form 11616.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
