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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 8550n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.a1 | 8550n1 | \([1, -1, 0, -21492, 1217916]\) | \(96386901625/18468\) | \(210362062500\) | \([2]\) | \(23040\) | \(1.1733\) | \(\Gamma_0(N)\)-optimal |
8550.a2 | 8550n2 | \([1, -1, 0, -19242, 1481166]\) | \(-69173457625/42633378\) | \(-485620821281250\) | \([2]\) | \(46080\) | \(1.5199\) |
Rank
sage: E.rank()
The elliptic curves in class 8550n have rank \(1\).
Complex multiplication
The elliptic curves in class 8550n 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 Cremona 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 Cremona labels.