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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 8640.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8640.bu1 | 8640cb1 | \([0, 0, 0, -2592, -50976]\) | \(-5971968/25\) | \(-8062156800\) | \([]\) | \(6912\) | \(0.75584\) | \(\Gamma_0(N)\)-optimal |
| 8640.bu2 | 8640cb2 | \([0, 0, 0, 6048, -268704]\) | \(8429568/15625\) | \(-45349632000000\) | \([]\) | \(20736\) | \(1.3051\) |
Rank
sage: E.rank()
The elliptic curves in class 8640.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 8640.bu do not have complex multiplication.Modular form 8640.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
