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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 20160.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.fj1 | 20160cl4 | \([0, 0, 0, -24492, 1474576]\) | \(68017239368/39375\) | \(940584960000\) | \([2]\) | \(32768\) | \(1.2431\) | |
| 20160.fj2 | 20160cl3 | \([0, 0, 0, -14412, -656336]\) | \(13858588808/229635\) | \(5485491486720\) | \([2]\) | \(32768\) | \(1.2431\) | |
| 20160.fj3 | 20160cl2 | \([0, 0, 0, -1812, 13984]\) | \(220348864/99225\) | \(296284262400\) | \([2, 2]\) | \(16384\) | \(0.89650\) | |
| 20160.fj4 | 20160cl1 | \([0, 0, 0, 393, 1636]\) | \(143877824/108045\) | \(-5040947520\) | \([2]\) | \(8192\) | \(0.54992\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20160.fj have rank \(0\).
Complex multiplication
The elliptic curves in class 20160.fj 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 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.
