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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 2550.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2550.bf1 | 2550be2 | \([1, 0, 0, -690638, -220971858]\) | \(3730569358698025/102\) | \(996093750\) | \([]\) | \(18000\) | \(1.6895\) | |
2550.bf2 | 2550be1 | \([1, 0, 0, -1628, 432]\) | \(19088138515945/11040808032\) | \(276020200800\) | \([5]\) | \(3600\) | \(0.88479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2550.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 2550.bf do not have complex multiplication.Modular form 2550.2.a.bf
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.