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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 8550.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.g1 | 8550f2 | \([1, -1, 0, -364167, -84494259]\) | \(468898230633769/5540400\) | \(63108618750000\) | \([2]\) | \(73728\) | \(1.7980\) | |
| 8550.g2 | 8550f1 | \([1, -1, 0, -22167, -1388259]\) | \(-105756712489/12476160\) | \(-142111260000000\) | \([2]\) | \(36864\) | \(1.4514\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.g have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.g do not have complex multiplication.Modular form 8550.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
