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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 154560.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.ej1 | 154560bw3 | \([0, 1, 0, -31485601, 38636594399]\) | \(13167998447866683762601/5158996582031250000\) | \(1352400000000000000000000\) | \([2]\) | \(23592960\) | \(3.3290\) | |
| 154560.ej2 | 154560bw2 | \([0, 1, 0, -14174881, -20119451425]\) | \(1201550658189465626281/28577902500000000\) | \(7491525672960000000000\) | \([2, 2]\) | \(11796480\) | \(2.9824\) | |
| 154560.ej3 | 154560bw1 | \([0, 1, 0, -14092961, -20368144161]\) | \(1180838681727016392361/692428800000\) | \(181516055347200000\) | \([2]\) | \(5898240\) | \(2.6358\) | \(\Gamma_0(N)\)-optimal |
| 154560.ej4 | 154560bw4 | \([0, 1, 0, 1825119, -62957851425]\) | \(2564821295690373719/6533572090396050000\) | \(-1712736722064782131200000\) | \([2]\) | \(23592960\) | \(3.3290\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.ej have rank \(1\).
Complex multiplication
The elliptic curves in class 154560.ej do not have complex multiplication.Modular form 154560.2.a.ej
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
