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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 91200.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.ce1 | 91200y4 | \([0, -1, 0, -244033, 46479937]\) | \(784767874322/35625\) | \(72960000000000\) | \([2]\) | \(589824\) | \(1.7362\) | |
| 91200.ce2 | 91200y3 | \([0, -1, 0, -76033, -7448063]\) | \(23735908082/1954815\) | \(4003461120000000\) | \([2]\) | \(589824\) | \(1.7362\) | |
| 91200.ce3 | 91200y2 | \([0, -1, 0, -16033, 651937]\) | \(445138564/81225\) | \(83174400000000\) | \([2, 2]\) | \(294912\) | \(1.3897\) | |
| 91200.ce4 | 91200y1 | \([0, -1, 0, 1967, 57937]\) | \(3286064/7695\) | \(-1969920000000\) | \([2]\) | \(147456\) | \(1.0431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91200.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 91200.ce do not have complex multiplication.Modular form 91200.2.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.
