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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 489762.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.bn1 | 489762bn2 | \([1, -1, 0, -548352, -153753768]\) | \(5182207647625/91449288\) | \(321786611597892168\) | \([2]\) | \(5898240\) | \(2.1556\) | \(\Gamma_0(N)\)-optimal* |
489762.bn2 | 489762bn1 | \([1, -1, 0, -792, -6898176]\) | \(-15625/5842368\) | \(-20557795949466048\) | \([2]\) | \(2949120\) | \(1.8091\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 489762.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 489762.bn do not have complex multiplication.Modular form 489762.2.a.bn
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.