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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 86640bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86640.q2 | 86640bn1 | \([0, -1, 0, -23376, -1894464]\) | \(-50284268371/26542080\) | \(-745685511045120\) | \([2]\) | \(245760\) | \(1.5580\) | \(\Gamma_0(N)\)-optimal |
86640.q1 | 86640bn2 | \([0, -1, 0, -412496, -101820480]\) | \(276288773643091/41990400\) | \(1179697781145600\) | \([2]\) | \(491520\) | \(1.9045\) |
Rank
sage: E.rank()
The elliptic curves in class 86640bn have rank \(0\).
Complex multiplication
The elliptic curves in class 86640bn do not have complex multiplication.Modular form 86640.2.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 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.