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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 65520.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.ce1 | 65520dz4 | \([0, 0, 0, -1129467, 462017194]\) | \(53365044437418169/41984670\) | \(125365552865280\) | \([4]\) | \(589824\) | \(2.0118\) | |
| 65520.ce2 | 65520dz3 | \([0, 0, 0, -164667, -15553046]\) | \(165369706597369/60703354530\) | \(181259245372907520\) | \([2]\) | \(589824\) | \(2.0118\) | |
| 65520.ce3 | 65520dz2 | \([0, 0, 0, -71067, 7116874]\) | \(13293525831769/365192100\) | \(1090457767526400\) | \([2, 2]\) | \(294912\) | \(1.6652\) | |
| 65520.ce4 | 65520dz1 | \([0, 0, 0, 933, 363274]\) | \(30080231/19110000\) | \(-57062154240000\) | \([2]\) | \(147456\) | \(1.3186\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65520.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 65520.ce do not have complex multiplication.Modular form 65520.2.a.ce
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.
