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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 65559.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65559.f1 | 65559d4 | \([1, 0, 1, -116865, -15386381]\) | \(37159393753/1053\) | \(5001859765773\) | \([2]\) | \(276480\) | \(1.5384\) | |
| 65559.f2 | 65559d3 | \([1, 0, 1, -32815, 2069123]\) | \(822656953/85683\) | \(407003181681603\) | \([2]\) | \(276480\) | \(1.5384\) | |
| 65559.f3 | 65559d2 | \([1, 0, 1, -7600, -220399]\) | \(10218313/1521\) | \(7224908550561\) | \([2, 2]\) | \(138240\) | \(1.1918\) | |
| 65559.f4 | 65559d1 | \([1, 0, 1, 805, -18679]\) | \(12167/39\) | \(-185254065399\) | \([2]\) | \(69120\) | \(0.84527\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65559.f have rank \(0\).
Complex multiplication
The elliptic curves in class 65559.f do not have complex multiplication.Modular form 65559.2.a.f
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.
