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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 8550.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.n1 | 8550k2 | \([1, -1, 0, -449667, 115926741]\) | \(882774443450089/2166000000\) | \(24672093750000000\) | \([2]\) | \(129024\) | \(2.0235\) | |
| 8550.n2 | 8550k1 | \([1, -1, 0, -17667, 3174741]\) | \(-53540005609/350208000\) | \(-3989088000000000\) | \([2]\) | \(64512\) | \(1.6770\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.n have rank \(1\).
Complex multiplication
The elliptic curves in class 8550.n do not have complex multiplication.Modular form 8550.2.a.n
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.
