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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 95550.et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95550.et1 | 95550ei4 | \([1, 0, 1, -1465126, 647733398]\) | \(189208196468929/10860320250\) | \(19964153392066406250\) | \([2]\) | \(2488320\) | \(2.4575\) | |
| 95550.et2 | 95550ei2 | \([1, 0, 1, -252376, -48605602]\) | \(967068262369/4928040\) | \(9059046530625000\) | \([2]\) | \(829440\) | \(1.9082\) | |
| 95550.et3 | 95550ei1 | \([1, 0, 1, -7376, -1565602]\) | \(-24137569/561600\) | \(-1032369975000000\) | \([2]\) | \(414720\) | \(1.5616\) | \(\Gamma_0(N)\)-optimal |
| 95550.et4 | 95550ei3 | \([1, 0, 1, 66124, 41358398]\) | \(17394111071/411937500\) | \(-757250545898437500\) | \([2]\) | \(1244160\) | \(2.1109\) |
Rank
sage: E.rank()
The elliptic curves in class 95550.et have rank \(0\).
Complex multiplication
The elliptic curves in class 95550.et do not have complex multiplication.Modular form 95550.2.a.et
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
