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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 20160fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.eg3 | 20160fj1 | \([0, 0, 0, -327, -1136]\) | \(82881856/36015\) | \(1680315840\) | \([2]\) | \(12288\) | \(0.46632\) | \(\Gamma_0(N)\)-optimal |
| 20160.eg2 | 20160fj2 | \([0, 0, 0, -2532, 48256]\) | \(601211584/11025\) | \(32920473600\) | \([2, 2]\) | \(24576\) | \(0.81289\) | |
| 20160.eg1 | 20160fj3 | \([0, 0, 0, -40332, 3117616]\) | \(303735479048/105\) | \(2508226560\) | \([2]\) | \(49152\) | \(1.1595\) | |
| 20160.eg4 | 20160fj4 | \([0, 0, 0, -12, 139984]\) | \(-8/354375\) | \(-8465264640000\) | \([2]\) | \(49152\) | \(1.1595\) |
Rank
sage: E.rank()
The elliptic curves in class 20160fj have rank \(1\).
Complex multiplication
The elliptic curves in class 20160fj do not have complex multiplication.Modular form 20160.2.a.fj
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
